Watanabe Keiichi 渡辺敬一

… Alternative Names

Researcher Number	10087083
Other IDs
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Affiliation (Current)	2019: 日本大学, 文理学部, 研究員 2019: 明治大学, 研究・知財戦略機構, 研究推進員(客員研究員)
Affiliation (based on the past Project Information) *help	2017: 日本大学, 文理学部, 上席研究員 2013 – 2016: 日本大学, 文理学部, 研究員 1997 – 2014: Nihon Univ., College of Humanities and Sciences, Professor, 文理学部, 教授 1989 – 1996: 東海大学, 理学部, 教授 1992: 東海大学, 情報数理, 教授 … More
Review Section/Research Field	Principal Investigator Algebra / Algebra / 代数学・幾何学 Except Principal Investigator Algebra / General mathematics (including Probability theory/Statistical mathematics) / Algebra / 代数学・幾何学 / Basic analysis
Keywords	Principal Investigator 有理特異点 / rational singularity / F-regular ring / Frobenius写像 / F-rational ring / Hilbert-Kunz multiplicity / Frobenius map / tight closure / 整閉イデアル / F-threshold … More Except Principal Investigator 特異点 / multiplier ideal / 密着閉包 / tight closure / jet scheme / arc space / 代数幾何学 / 重複度 / singularities / discrepancy / singularity / 有理特異点 / F-threshold / フィルター付きブロウイングアップ / フロベニウス写像 / 特異点解消 / 乗数イデアル / geometric genus / multiplicity / フラクタル / グラフ理論 / 組合せ論 / 交グラフ / 弧空間 / ジェットスキーム / 幾何種数 / 代数的スタック / rational singularity / graded ring / 可換環論 / Algebraic Geometry / Rees代数 / Bass orders / 代数幾何 / F-特異点 / 判定イデアル / 正標数 / Rees環 / F-singularity / algebraic geometry / Rees algebra / toric variety / 3次元端末特異点 / resolution of singularities / filtered blowing-up / Hilbert-Kunz重複度 / F-regular / Hilbert-Kunz multiplicity / 2変数 / 複素力学系 / 複素共役 / カオス / チェビシェフ多項式 / 不動点 / 2周期点 / Shifted Complex / 系統樹の最節約復元 / エルホ(el-tree) / NP-完全問題 / ジャンプナンバー問題 / 教授順序の最適性 / ボンド束 / 反鎖交数 / 階層環 / upper bound graph / lower bound graph / edge clique cover / poset / 双有理幾何学 / ジェット空間 / lc-threshold / integrally closed ideal / log-canonical threshold / integnally closedjlul / ゴレンスタイン性 / 基本サイクル / 極大イデアルサイクル / ブロウイングアップ / 2次元星型特異点 / 単純K3特異点 / 非退化完全交差式 / 中心フィルトレーション / F-thresholds / 重複度予想 / 超曲面特異点 / simple K3特異点 / ニュートン境界 / ベロネーゼ環 / 字数付き環 / exceptional log canonical singularity / stack / 極小対数的食い違い数 / 食い違い数 / Frobenius 射 / log-canonical singularity / データベース / 線形代数学 / アルゴリズム / 教育用ソフト / 状態監視保全 / マルコフ行列 / TP_2 / monotone likelihood / 代数多様体 / 代数多様体の分類 / Kahler多様体 / 共形場理論 / 安定層 / ベクトル束 / モデュライ / 代数多様体の変形 / モデュライ理論 / ホッジ理論 / 算術的代数幾何学 / 代数様体 / モジュライ / 算術的代数多様体 / Hodge-理論 / 放物束 / Algebraic Variety / Classification of Algebraic Varieties / Kahler Manifold / Conformal Field Theory / Stable Sheaves / Vector Bundle / Moduli / 局所環 / Cohen-Maculay加群 / Frobenius代数 / Zarisikiの問題 / Cohen-Macaulay加群 / Ress代数 / Zariskiの問題 / Cohen-Macaulay環 / Gorenstein環 / 有限次元多元環 / 整環 / 表現型 / 有限次元多元環の表現論 / local rings / Cohen-Macaulay modules / Rees algebras / Frobenius algebras / Zariski's problem / 0次元完全交差環 / 0次元ゴレンスタイン環 / 一般元 / レフシェツ条件 / 一次元波動方程式 / Lissajuus境界条件 / ディオファントス近似不等式 / 準周期解 / O次元完全交差環 / O次元ゴレンスタイン環 / Lissajous境界条件 / 弦の振動 / 1次元波動方程式 / 周期的に動く境界条件 / Diophantine近似 / Denjoy-Herman-Yoccoz理論 / 可換代数 / アルチン環 / ゴレンスタイン環 / Hard Lefschetz / Catalecticant / Hessian / 生成系 / Artinian complete intersection / Artinian Gorenstein algebra / general element / Lefschetz condition / one-dimensional wave equation / Lissajous boundary condition / Diophantine inequality / quasiperiodic solution / 数論 / 環論 / 群論 / 表現論 / 数論的幾何学 / 代数学 / 整数論 / 解析数論 / Number Theory / Ring Theory / Group Theory / Representation Theory / エルゴード理論 / ペロン-フロベニウス作用素 / 乱数 / ブラウン運動 / スペクトル / Perron-Frobenius作用素 / エルゴード性 / 混合性 / ergodic theory / Perron-Frobenius Operator / fractal / random number / Brownian motion / 密着閉包(I-密着閉包) / Subadditivity / 随伴束 / 記号的ベキ乗 / F-正則 / F-正則(F-regular) / F-有理(F-rational) / Tight closure / test ideal / positive characteristic / commutative algebra / jet scjeme / moduli space / integral closed / complete intersection / multipier ideal / plurigenera / moduli spase / 多重種数 / Gluck手術 / 局所環の位数関数 / 付随次数付き環 / フィルター付ブロウイングアップ / フリップの存存定理 / 双正則同形問題 / 4次元多様体 / Dehn手術 / plurigenus / 3-dimensional terminal singularities / Gluck surgery / algebraic stacks / order function of local rings / associated graded rings / F正則性 / F有理性 / ブローアップ / Ress環 / F-rational / Frobenius map / blow-up / F-純閾値 / トーリック多様体 / トロピカル幾何 / 対数的標準閾値 / CCI曲面 / トロピカル・トーリック多様体 / Buchsbaum斉次代数 / P-フラクタル / F-pure threshold / tropical geometry / F正則環 / Buchsbaum環 / Stanley-Reisner環 / Buchsbaum ring / Stanley-Reisner ring / Cohen-Macaulay / F-pure / Alexander duality / lineal resolution / ヒルベルト・クンツ重複度 / 線型自由分解 / スタンレー・リースナー環 / ブックスバウム環 / Buchsbaum rings / Stanley・Reisner rings / 楕円型特異点 / 次元特異点 / 普遍アーベル被覆 / 2次元特異点 / ベロネーゼ部分環 / 完全交叉性 / 2次元楕円型特異点 / 整閉イデアルの対数的特異点解消 / multiplierイデアル / implicit differential systems / 3次元端末的特異点 / elliptic singularity / 3-dimensional terminal singularity / 2-dimensional singularity / universal abelican covering / 楕円曲線のMordell-Weil群の階数について Less

Commutative Ring Theory of SingularitiesPrincipal Investigator
- Principal Investigator
  
  WATANABE Keiichi
- Project Period (FY)
  2014 – 2017
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Nihon University
Commutative Ring Theory of Singularities of Algebraic VarietiesPrincipal Investigator
- Principal Investigator
  
  WATANABE Kei-ichi
- Project Period (FY)
  2011 – 2013
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Nihon University
Singularities on algebraic varieties
- Principal Investigator
  
  ISHII Shihoko
- Project Period (FY)
  2010 – 2014
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  The University of Tokyo
Characteristic p method in singularity theoryPrincipal Investigator
- Principal Investigator
  
  WATANABE Keichi
- Project Period (FY)
  2008 – 2010
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Nihon University
Research on the singularities of a variety
- Principal Investigator
  
  ISHII Shihoko
- Project Period (FY)
  2006 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Tokyo Institute of Technology
Classification of isolated singularities by means of algebraic geometric studies of invariants
- Principal Investigator
  
  TOMARI Masataka
- Project Period (FY)
  2006 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Nihon University
Singurality Theory and Frobenius MorphismPrincipal Investigator
- Principal Investigator
  
  WATANABE Keiichi
- Project Period (FY)
  2005 – 2007
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Nihon University
Applications of tight closure and F-singularity to algebraic geometry
- Principal Investigator
  
  HARA Nobuo
- Project Period (FY)
  2004 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Tohoku University
Research for multiplicities and tight closures on singular points of positive characteristic
- Principal Investigator
  
  YOSHIDA Kenichi
- Project Period (FY)
  2004 – 2006
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Nagoya University
Filtered blowing-up of local rings and algebraic geometric classification of singularities
- Principal Investigator
  
  TOMARI Masataka
- Project Period (FY)
  2004 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Nihon University
Research on singularities of a variety
- Principal Investigator
  
  ISHII Shihoko
- Project Period (FY)
  2002 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Tokyo Institute of Technology
Filtered blowing-up of singularities and algebraic geometric properties of tangent cone
- Principal Investigator
  
  TOMARI Masataka
- Project Period (FY)
  2002 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Nihon University
  Kanazawa University
On ring-theoretical properties of blow-up rings over singular points in positive characteristic
- Principal Investigator
  
  YOSHIDA Ken-ichi
- Project Period (FY)
  2002 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Nagoya University
整閉イデアルの族の研究Principal Investigator
- Principal Investigator
  
  渡辺敬一
- Project Period (FY)
  2001 – 2003
- Research Category
  
  Grant-in-Aid for Exploratory Research
- Research Field
  
  Algebra
- Research Institution
  Nihon University
Commutative ring theory and singularity theoryPrincipal Investigator
- Principal Investigator
  
  WATANABE Keiichi
- Project Period (FY)
  2001 – 2004
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Nihon University
Algebro-Geometric Method in Commutative Algebra
- Principal Investigator
  
  HARA Nobuo
- Project Period (FY)
  2001 – 2003
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Tohoku University
Study of relations and applications of Arithmetic Geometry to branches of Algebra
- Principal Investigator
  
  MORITA Yasuo
- Project Period (FY)
  2000 – 2002
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  Tohoku University
Research on ergodic theory and Perron-Frobenius operator
- Principal Investigator
  
  MORI Makoto
- Project Period (FY)
  2000 – 2001
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Basic analysis
- Research Institution
  Nihon University
Characteristic p method in singularity theoryPrincipal Investigator
- Principal Investigator
  
  WATANABE Keiichi
- Project Period (FY)
  1998 – 2000
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  NIHON UNIVERSITY
Upper bound graphとposetの関連について
- Principal Investigator
  
  土屋守正
- Project Period (FY)
  1995
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Tokai University
Applications of Frobenius map to Commutative Ring Theory and Algebraic GeometryPrincipal Investigator
- Principal Investigator
  
  WATANABE Keiichi
- Project Period (FY)
  1995 – 1997
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  NIHON UNIVERSITY
  Tokai University
F-rational Ringの研究Principal Investigator
- Principal Investigator
  
  渡辺敬一
- Project Period (FY)
  1994
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Tokai University
Study on algebras and their representations
- Principal Investigator
  
  AKIBA Tomoharu, YOSHINO Yuji
- Project Period (FY)
  1994 – 1996
- Research Category
  
  Grant-in-Aid for Scientific Research (A)
- Research Field
  
  Algebra
- Research Institution
  KYOTO UNIVERSITY
Commutative Artinian Algebras
- Principal Investigator
  
  YAMAGUCHI Masaru, 渡辺純三
- Project Period (FY)
  1994 – 1996
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Tokai University
Frobenius写像の特異点への作用Principal Investigator
- Principal Investigator
  
  渡辺敬一
- Project Period (FY)
  1993
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  Algebra
- Research Institution
  Tokai University
数え上げ組合せ論の鎖数の研究
- Principal Investigator
  
  成嶋弘
- Project Period (FY)
  1992
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Tokai University
Algebra and Geometry on Algebraic Varieties
- Principal Investigator
  
  MARUYAMA Masaki
- Project Period (FY)
  1992 – 1994
- Research Category
  
  Grant-in-Aid for Co-operative Research (A)
- Research Field
  
  代数学・幾何学
- Research Institution
  KYOTO UNIVERSITY
Intersection Graphの研究
- Principal Investigator
  
  土屋守正
- Project Period (FY)
  1991
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Tokai University
有理特異点とFrobenius写像の作用Principal Investigator
- Principal Investigator
  
  渡辺敬一
- Project Period (FY)
  1990
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  Tokai University
エントロピ-とブラクタルと無限行列の関連
- Principal Investigator
  
  内村桂輔
- Project Period (FY)
  1989
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Tokai University
状態監視保全の数理モデルとその最適性に関する研究
- Principal Investigator
  
  鈴木和幸
- Project Period (FY)
  1988
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Tokai University
データベースを土台にした大学の数学における自習システムと言語の開発
- Principal Investigator
  
  永瀬輝男
- Project Period (FY)
  1987
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Tokai University
On the Rang of Mordell-Well group of Elliptic curves.
- Principal Investigator
  
  MIWA Megumu
- Project Period (FY)
  1985 – 1986
- Research Category
  
  Grant-in-Aid for General Scientific Research (C)
- Research Field
  
  代数学・幾何学
- Research Institution
  NAGOYA INSTITUT OF TECHNOLOGY

[Book] 可換環論2011
- Author(s)
  後藤四郎，渡辺敬一
- Total Pages
  350
- Publisher
  日本評論社
- Data Source
  KAKENHI-PROJECT-23540059
[Book] 群論の進化2004
- Author(s)
  堀田, 渡辺, 庄司, 三町
- Total Pages
  445
- Publisher
  朝倉書店
- Data Source
  KAKENHI-PROJECT-14340005
[Book] 環と体2002
- Author(s)
  渡辺敬一
- Total Pages
  180
- Publisher
  朝倉書店
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] A characterization of two-dimensional rational singularities via Core of ideals2018
- Author(s)
  T. Okuma, K. Watanabe, K. Yoshida
- Journal Title
  
  Journal of Algebra
  
  Volume: 499 Pages: 450-468
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26400053
[Journal Article] Rees algebras and p_g-ideals in a two-dimensional normal local domain2017
- Author(s)
  T.Okuma, K.Watanabe, K.YOshida
- Journal Title
  
  Proc. Americam Math. Soc.
  
  Volume: 145 Pages: 39-47
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26400053
[Journal Article] Good ideals and p_g-ideals in two-dimensional normal singularities2016
- Author(s)
  T.Okuma, K. Watanabe, K. Yoshida
- Journal Title
  
  manuscripta mathematica
  
  Volume: 未定 Pages: 499-520
- DOI
  10.1007/s00229-016-0821-7
- Peer Reviewed / Open Access / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-26400053, KAKENHI-PROJECT-26400064, KAKENHI-PROJECT-15H02057, KAKENHI-PROJECT-16K05110
[Journal Article] Some computations of generalized Hilbert-Kunz function and multiplicity,2016
- Author(s)
  H. Dao, K. Watanabe
- Journal Title
  
  Proc. Amer. Math. Soc.
  
  Volume: 144 Pages: 3199-3206
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26400053
[Journal Article] Upper bound of multiplicity of F-rational rings and F-pure rings,2015
- Author(s)
  C. Huneke　and K. Watanabe
- Journal Title
  
  Proc. Amer.　Ｍａｔｈ．　Ｓｏｃ．
  
  Volume: １４２ Pages: 5021-5026
- Acknowledgement Compliant / Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26400053
[Journal Article] Classification of 2-dimensional normal graded hypersurfaces2014
- Author(s)
  K. Watanabe
- Journal Title
  
  Bull. Brazilian Math. Soc.
  
  Volume: 45 Pages: 887-920
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26400053
[Journal Article] F 特異点 -- 正標数の手法の特異点論への応用2014
- Author(s)
  高木俊輔 - 渡辺敬一
- Journal Title
  
  数学
  
  Volume: 66 Pages: 1-30
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26400053
[Journal Article] Ulrich ideals and modules2014
- Author(s)
  S. Goto, Kazuho Ozeki, , Ryo Takahashi, Kei-ichi Watanabe, Ken-ichi . Yoshida
- Journal Title
  
  Mathematical Proceedings of the Cambridge Philosophical Society
  
  Volume: vol.156 Pages: 137-166
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] F-thresholds vs. a-invariants for homogeneous toric rings2014
- Author(s)
  Daisuke Hirose, Kei-ichi Watanabe, Ken-ichi . Yoshida
- Journal Title
  
  Communications in Algebra
  
  Volume: vol 42 Pages: 2704-2720
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Upper bound of multiplicity of F-rational rings and F-pure rings,2014
- Author(s)
  C. Huneke, K. Watanabe
- Journal Title
  
  Proc. Amer. Math. Soc.
  
  Volume: To appear
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] F特異点--正標数の手法の特異点論への応用2014
- Author(s)
  高木俊輔・渡辺敬一
- Journal Title
  
  「数学」(日本数学会)
  
  Volume: 66巻 Pages: 1-30
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Ulrich ideals and modules2014
- Author(s)
  S. Goto, K. Ozeki, R. Takahashi, K. Watanabe, K. Yoshida
- Journal Title
  
  Mathematical Proceedings of the Cambridge Philosophical Society
  
  Volume: 156 Pages: 137-166
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Ulrich ideals and modules2014
- Author(s)
  S. Goto, K. Ozeki, R. Takahashi, K. Watanabe, K. Yoshida
- Journal Title
  
  Mathematical Proceedings of the Cambridge Philosophical Society
  
  Volume: 156 Pages: 137-166
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26400053
[Journal Article] F-thresholds vs. a-invariants for homogeneous toric rings2014
- Author(s)
  D. Hirose, K. Watanabe, K. Yoshida
- Journal Title
  
  Communications in Algebra
  
  Volume: 42 Pages: 2704-2720
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Jet schemes of homogeneous hypersurfaces2012
- Author(s)
  S.Ishii（with K-i. Watanabe, A.Sannai)
- Journal Title
  
  Singularities in Geometry and Topology, Strasbourg 2009, IRMA Lectures in Mathematics and Theoretical Physics
  
  Volume: 20 Pages: 39-49
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340004
[Journal Article] A variant of Wang's theorem,2012
- Author(s)
  Kei-ichi Watanabe, Ken-ichi Yoshida
- Journal Title
  
  Journal of Algebra
  
  Volume: 369 Pages: 129-145
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Genus of numerical semigroups generated by three elements,2012
- Author(s)
  K.-i. Watanabe (with Hirokatsu Nari, Takahiro Numata).
- Journal Title
  
  J. of Algebra
  
  Volume: 358 Pages: 67-73
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340004
[Journal Article] Jet schemes of homogeneous hypersurfaces,2012
- Author(s)
  Shihoko Ishii, Akiyoshi Sannnai, Kei-ichi Watanabe
- Journal Title
  
  IRMA Lectures in Mathematics and Theoretical Physics , European Mathematical Society
  
  Volume: 20 Pages: 39-49
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Genus of numerical semigroups generated by three elements,2012
- Author(s)
  H. Nari, T. Numata, K. Watanabe
- Journal Title
  
  Jouranal of Algebra
  
  Volume: 358 Pages: 67-73
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Genus of numerical semigroups generated by three elements,2012
- Author(s)
  Hirokatsu Nari, Takahiro Numata, Kei-ichi Watanabe
- Journal Title
  
  Journal of Algebra
  
  Volume: 358 Pages: 67-73
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Genus of numerical semigroups generated by three elements2012
- Author(s)
  Hirokatsu Nari, Takahiro Numata, Kei-ichi Watanabe
- Journal Title
  
  J. of Algebra
  
  Volume: vol.358 Pages: 67-73
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] A variant of Wang's theorem2012
- Author(s)
  K.-i. Watanabe (with K. Yoshida),
- Journal Title
  
  J. of Algebra
  
  Volume: 369 Pages: 129-145
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340004
[Journal Article] A variant of Wang's theorem2012
- Author(s)
  Kei-ichi Watanabe, Ken-ichi . Yoshida
- Journal Title
  
  J. of Algebra
  
  Volume: vol.369 Pages: 129-145
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Jet schemes of homogeneous hypersurfaces, "Singularities in Geometry and Topology, Strasbourg 2009"2012
- Author(s)
  Shihoko Ishii, Akiyoshi Sannai, Kei-ichi Watanabe
- Journal Title
  
  IRMA Lectures in Mathematics and Theoretical Physics 20, European Mathematical Society
  
  Pages: 39-49
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Multiplicity bounds in graded ring2011
- Author(s)
  C.Huneke, S.Takagi, K.Watanabe
- Journal Title
  
  Kyoto J.math.
  
  Volume: 51 Pages: 127-147
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340004
[Journal Article] F-signature of graded Gorenstein rings2011
- Author(s)
  K.Watanabe, A.Sannai
- Journal Title
  
  J.Pure and Appl.Algebra. in press
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Coefficient ideal of ideals generated by monomials2011
- Author(s)
  Satoshi Ohnishi, Kei-ichi Watanabe
- Journal Title
  
  Communications in Algebra
  
  Volume: vol.39 Pages: 1563-1576
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Coefficient ideal of ideals generated by monomials2011
- Author(s)
  K.Watanabe, S.Ohnishi
- Journal Title
  
  Comm.Alg
  
  Volume: 39 Pages: 1563-1576
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22340004
[Journal Article] F-signature of graded Gorenstein rings2011
- Author(s)
  K.Watanabe (A.Sannai)
- Journal Title
  
  J.Pure and Appl.Algebra
  
  Volume: (in press)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Coefficient ideal of ideals generated by monomials2011
- Author(s)
  K.Watanabe, S.Ohnishi
- Journal Title
  
  Communications in Algebra. in press
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- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Multiplicity bounds in graded rings2011
- Author(s)
  K.Watanabe, C.Huneke, S.Takagi
- Journal Title
  
  Kyoto Journal of Mathematics. in press
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Coefficient ideal of ideals generated by monomials2011
- Author(s)
  K.Watanabe (S.Ohnishi)
- Journal Title
  
  Communications in Algebra
  
  Volume: (in press)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Pseudo-symmetric and atomic numerical semigroups generated by three elements2011
- Author(s)
  K.Watanabe, H.Nari, T.Numata
- Journal Title
  
  Proc.Inst.Natural Sci., Nihon Univ. 46 in press
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Multiplicity bounds in graded rings2011
- Author(s)
  K.Watanabe (C.Huneke, S.Takagi)
- Journal Title
  
  Kyoto Journal of Mathematics
  
  Volume: (in press)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] F-signature of graded Gorenstein rings2011
- Author(s)
  A.Sannnai, K.Watanabe
- Journal Title
  
  J.Pure and Appl.Algebra. vol.215
  
  Pages: 2190-2195
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540050
[Journal Article] Multiplicity bounds in graded rings2011
- Author(s)
  Craig Huneke, S. Takagi, Kei-ichi Watanabe
- Journal Title
  
  Kyoto Journal of Mathematics
  
  Volume: vol.51 Pages: 127-147
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Pseudo-symmetric and atomic numerical semigroups generated by three elements2011
- Author(s)
  K.Watanabe (H.Nari, T.Numata)
- Journal Title
  
  Proc.Inst.Natural Sci., Nihon Univ.
  
  Volume: 46(in press)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Multiplicity bounds in graded rings2011
- Author(s)
  C.Huneke-S.Takagi-K.Watanabe
- Journal Title
  
  Kyoto Journal of Mathematics
  
  Volume: 51 Pages: 127-147
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540050
[Journal Article] F-signature of graded Gorenstein rings2011
- Author(s)
  Akiyoshi Sannai, Kei-ichi Watanabe
- Journal Title
  
  J. Pure and Appl. Algebra
  
  Volume: vol.215 Pages: 2190-2195
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Coefficient ideal of ideals generated by monomials, To appear in Communications in Algebra2011
- Author(s)
  S.Ohnishi, K.Watanabe
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540050
[Journal Article] Multiplicity bounds in graded rings, Kyoto Journal of Mathematics2011
- Author(s)
  C. Huneke, S. Takagi, K. Watanabe
- Journal Title
  
  Kyoto Journal of Mathematics
  
  Volume: 51 Pages: 127-147
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Multiplicity bounds in graded rings2011
- Author(s)
  C.Huneke, S.Takagi, K.Watanabe
- Journal Title
  
  Kyoto Journal of Mathematics vol.51, No.1
  
  Pages: 127-147
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540050
[Journal Article] Multigraded rings, Diagonal subalgebras and rational singularities2009
- Author(s)
  K. Kurano, E. Sato, A. Singh, K.-i. Watanabe
- Journal Title
  
  J. of Algebra 322
  
  Pages: 3248-3267
- Data Source
  KAKENHI-PROJECT-18540051
[Journal Article] Multigraded rings, diagonal subalgebras, and rational singularities2009
- Author(s)
  K.Watanabe (K.Kurano, E.Sato, A.Singh)
- Journal Title
  
  J.of Algebra
  
  Volume: 322 Pages: 3248-3267
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Multigraded rings, diagonal subalgebras, and rational singularities2009
- Author(s)
  K.Kurano, E.Sato, A.Singh K.Watanabe
- Journal Title
  
  Journal of Algebra 322
  
  Pages: 3248-3267
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540050
[Journal Article] Multigraded rings, diagonal subalgebras and rational singularities2009
- Author(s)
  K.Kurano, E.Sato, A.Singh, K.-i.Watanabe
- Journal Title
  
  J.of Algebra 322
  
  Pages: 3248-3267
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540051
[Journal Article] Multigraded rings, diagonal subalgebras, and rational singularities2009
- Author(s)
  K.Kurano, E.Sato, A.Singh., K.Watanabe
- Journal Title
  
  J.of Algebra vol.322
  
  Pages: 3248-3267
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540050
[Journal Article] Multigraded rings, diagonal subalgebras, and rational singularities2009
- Author(s)
  K.Watanabe, K.Kurano, E.Sato, A.Singh
- Journal Title
  
  J.of Algebra 322
  
  Pages: 3248-3267
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Coefficient ideals of ideals in k[X, Y] generated by monomials2008
- Author(s)
  S. Ohnishi, K. Watanabe
- Journal Title
  
  Proc. Inst. Natural Sci., Nihon Univ. 43
  
  Pages: 347-352
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540050
[Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds2008
- Author(s)
  C. Huneke, M. Mustata, S. Takagi, K. Watanabe
- Journal Title
  
  Michigan Math. J. 57
  
  Pages: 463-483
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540051
[Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds2008
- Author(s)
  C.Huneke, M.Mustata, S Takagi, K.Watanabe
- Journal Title
  
  Michigan Math.J. vol.57
  
  Pages: 463-483
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540050
[Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds2008
- Author(s)
  C., Huneke, M., Mustata, S., Takagi, K., Watanabe
- Journal Title
  
  Michigan Mathematical Journal (to appear in)
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] Coefficient ideals of ideals in $k[X, Y]$ generated by monomials2008
- Author(s)
  K.Watanabe, S.Ohnishi
- Journal Title
  
  Proc.Inst.Natural Sci., Nihon Univ. 43
  
  Pages: 347-352
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds2008
- Author(s)
  渡辺敬一, C. Huneke, M. Mustata and S, Takagi
- Journal Title
  
  to appear in Michigan Math. J. (掲載決定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds2008
- Author(s)
  C. Huneke, M. Mustata, S. Takagi, K. Watanabe
- Journal Title
  
  Michigan Math. J. 57
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds,2008
- Author(s)
  C. Huneke, M. Mustata, S. Takagi), K. Watanabe
- Journal Title
  
  Michigan Math. J To appear
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds2008
- Author(s)
  K.Watanabe, C.Huneke, M.Mustata, S.Takagi
- Journal Title
  
  Michigan Math.J. 57
  
  Pages: 463-483
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] F-thresholds,tight closure,integral closure,and multiplicity bounds2008
- Author(s)
  C. Huneke, M. Mustata S. Takagi, K. Watanabe
- Journal Title
  
  Michigan Math.J. (印刷中)
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds2008
- Author(s)
  C. Huneke. M. Mustata, S, Takagi, K. Watanabe
- Journal Title
  
  Michigan Math. J. 57
  
  Pages: 463-483
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540050
[Journal Article] Coefficient ideals of ideals in $k[X,Y]$ generated by monomials2008
- Author(s)
  渡辺敬一
- Journal Title
  
  to appear in Proc. Inst. Natural Sci., Nihon Univ. 43(掲載決定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds2008
- Author(s)
  C. Huneke, M. Mustata, S. Takagi and K. Watanabe
- Journal Title
  
  Michigan Math. J. 57
  
  Pages: 463-483
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Coefficient ideals of ideals in k[X,Y]generated by monomials2008
- Author(s)
  S. Ohnishi, K. Watanabe
- Journal Title
  
  Proc.Inst.Natural science, Nihon Univ 43
  
  Pages: 347-352
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] Totally reflexive modules constructed from smooth pro jective curves of genus g≧ 22007
- Author(s)
  R., Takahashi, K.Watanabe
- Journal Title
  
  Archiv der Mathematik 89
  
  Pages: 60-67
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds2007
- Author(s)
  K. i. Watanabe, C. Huneke, M. Mustata, S. Takagi
- Journal Title
  
  Michigan Math. J. vol.57
  
  Pages: 60-67
- Data Source
  KAKENHI-PROJECT-18540051
[Journal Article] Totally reflexive modules constructed from smooth projective curves of genus g〓22007
- Author(s)
  R. Takahashi, K. Watanabe
- Journal Title
  
  Archiy der Mathematik 89
  
  Pages: 60-67
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] Totally reflexive modules constructed from smooth projective curves of genus2007
- Author(s)
  渡辺敬一
- Journal Title
  
  Archiv der Mathematik 89
  
  Pages: 60-67
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Totally reflexive modules constructed from smooth projective curves of genus g〓22007
- Author(s)
  R. Takahashi and K. Watanabe
- Journal Title
  
  Archiv der Mathematik 89
  
  Pages: 60-67
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] Totally reflexive modules constructed from smooth projective curves of genus g \geq 22007
- Author(s)
  K. i. Watanabe, R. Takahashi
- Journal Title
  
  Archiv der Mathematik 89
  
  Pages: 60-67
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540051
[Journal Article] Totally reflexive modules constructed from smooth projective curves of genus g geq 22007
- Author(s)
  K. i. Watanabe, R. Takahashi
- Journal Title
  
  Archiv der Mathematik 89
  
  Pages: 60-67
- Data Source
  KAKENHI-PROJECT-18540051
[Journal Article] Totally reflexive modules constructed from smooth projective curves of genus $g\geq2$2007
- Author(s)
  K.Watanabe, R.Takahashi
- Journal Title
  
  Archiv der Mathematik 89
  
  Pages: 60-67
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Adjacent integrally closed ideals in 2-dimensional regular local rings2006
- Author(s)
  K.Watanabe, S.Noh
- Journal Title
  
  J.of Algebra 302
  
  Pages: 156-166
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Adjacent integrally closed ideals in 2-dimensional regular local rings.2006
- Author(s)
  S. Noh, K.-i. Watanabe
- Journal Title
  
  J. of Algebra 300
  
  Pages: 156-166
- Data Source
  KAKENHI-PROJECT-18540051
[Journal Article] Adjacent integrally closed ideals in 2-dimensional regular local rings2006
- Author(s)
  Sunsook Noh, Kei-ichi Watanabe
- Journal Title
  
  Journal of Algebra 302
  
  Pages: 156-166
- Data Source
  KAKENHI-PROJECT-16540021
[Journal Article] Adjacent integrally closed ideals in 2-dimensional regular local rings2006
- Author(s)
  S., Noh, K., Watanabe
- Journal Title
  
  J. of Algebra 302
  
  Pages: 156-166
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] Adjacent integrally closed ideals in 2-dimensional regular local rings2006
- Author(s)
  S. Noh, K. Watanabe
- Journal Title
  
  Journal of Algebra 302
  
  Pages: 156-166
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] Adjacent integrally closed ideals in 2-dimensional regular local rings,2006
- Author(s)
  S.Noh, K.Watanabe
- Journal Title
  
  Journal of Algebra 302
  
  Pages: 156-166
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] Adjacent integrally closed ideals in 2-dimensional regular local rings.2006
- Author(s)
  S.Noh, K, -i.Watanabe
- Journal Title
  
  J. of Algebra 300
  
  Pages: 156-166
- Data Source
  KAKENHI-PROJECT-18540051
[Journal Article] Adjacent integrally dosed idecls in 2-dimeasinul regular localrin2006
- Author(s)
  渡辺敬一, S. Noh
- Journal Title
  
  Joural of Algebra 302
  
  Pages: 156-166
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Hilbert-Kunz multiplicity of three-dimensional local rings2005
- Author(s)
  K.-i.Watanabe, K.Yoshida
- Journal Title
  
  Nagoya Math.J. 177
  
  Pages: 47-75
- Data Source
  KAKENHI-PROJECT-16540021
[Journal Article] Hilbert-Kunz multiplicity of three-dimensional local rings2005
- Author(s)
  Kei-ichi Watanabe, Ken-ichi Yoshida
- Journal Title
  
  Nagoya Math. J. 177
  
  Pages: 47-75
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540021
[Journal Article] F-thresholds and Berstein-Sato polynomials,2005
- Author(s)
  M.Mustata, S.Takagi, K.Watanabe
- Journal Title
  
  Proc.4ECM Stockholm 2004
  
  Pages: 341-364
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] Hilbert-Kunz multiplicity of three-dimensional local Hngs2005
- Author(s)
  K.-i.Watanabe, K.Yoshida
- Journal Title
  
  Nagoya Math J 177
  
  Pages: 47-75
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540005
[Journal Article] Hilbert-Kunz multiplicity of three dimensional local Rings2005
- Author(s)
  渡辺敬一, 吉田健一
- Journal Title
  
  Nagoya Math.J. 177
  
  Pages: 47-75
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] Hilbert-Kunz multiplicity of three-dimensional local rings2005
- Author(s)
  K.-i.Watanabe, K.-i.Yoshida
- Journal Title
  
  Nagoya Math. J. 177
  
  Pages: 47-75
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540043
[Journal Article] Hilbert-Kunz multiplicity of three dimensional local rings,2005
- Author(s)
  K.Watanabe, K.Yoshida
- Journal Title
  
  Nagoya Math.J. 177
  
  Pages: 47-75
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] Hilbert-Kunz multiplicity of three-dimensional local rings2005
- Author(s)
  K.-i.Watanabe, K.-i.Yoshida
- Journal Title
  
  Nagoya Math.J. 177
  
  Pages: 47-75
- Data Source
  KAKENHI-PROJECT-16540043
[Journal Article] Hilbert-Kunz multiplicity of three-dimensional local rings2005
- Author(s)
  K.-i.Watanabe, K.-i.Yoshida
- Journal Title
  
  Nagoya Math.J. vol.177
  
  Pages: 47-75
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16540043
[Journal Article] Hilbert-Kunz multiplicity of three-dimensional local rings2005
- Author(s)
  K., Watanabe, K., Yoshida
- Journal Title
  
  Nagoya Math. J 177
  
  Pages: 47-75
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] Hilbert-Kunz multiplicity of three dimensional local rings2005
- Author(s)
  K.Watanabe, K.Yoshida
- Journal Title
  
  Nagoya Math.J. vol.177
  
  Pages: 47-75
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] F-thresholds and Bernstein-Sato polynomials2005
- Author(s)
  K.-i.Watanabe, M.Mustata, S.Takagi
- Journal Title
  
  European Congress of Mathematics, Eur.Math.Soc., Zurich
  
  Pages: 341-364
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16540005
[Journal Article] Hilbert-Kunz multiplicity of three dimensional local rings2005
- Author(s)
  渡辺敬一
- Journal Title
  
  Nagoya Math. J. 177
  
  Pages: 47-7775
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] Hilbert-Kunz multiplicity of three-dimensional local rings2005
- Author(s)
  K.-i.Watanabe, K.Yoshida
- Journal Title
  
  Nagoya Math.J. 177
  
  Pages: 47-75
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16540005
[Journal Article] Hilbert-Kunz multiplicity of three dimensional local rings2005
- Author(s)
  K-i.Watanabe, k.Yoshida
- Journal Title
  
  Nagoya Mathematical Journal 177
  
  Pages: 47-75
- Data Source
  KAKENHI-PROJECT-16540005
[Journal Article] F-thresholds and Bernstein-Sato polynomial2005
- Author(s)
  M.Mustata, S.Takagi, K.Watanabe
- Journal Title
  
  Europian Congress of Mathematics
  
  Pages: 341-364
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540005
[Journal Article] Hilbert-Kunz multiplicity of three dimensional local rings,2005
- Author(s)
  K.Watanabe
- Journal Title
  
  Nagoya Math.J. 177
  
  Pages: 47-75
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] Hilbert-Kunz multiplicity of three-dimensional local rings2005
- Author(s)
  K. Watanabe, K. Yoshida
- Journal Title
  
  Nagoya Math.J. 177
  
  Pages: 47-75
- Description
  「研究成果報告書概要(和文)」より
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] Hilbert-Kunz multiplicity of three dimensional local Rings2005
- Author(s)
  渡辺敬一, 吉田健一
- Journal Title
  
  Nagoya Math. J. 177
  
  Pages: 47-75
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] Minimal relative Hilbert-Kunz multiplicity2004
- Author(s)
  K.Watanabe, K.Yoshida
- Journal Title
  
  Illinois J.Math. 48
  
  Pages: 273-294
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] Minimal relative Hilbert-Kunz multiplicity2004
- Author(s)
  Kei-ichi Watanabe, Ken-ichi Yoshida
- Journal Title
  
  Illinois J. Math. 48
  
  Pages: 273-294
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540021
[Journal Article] O F-pure thresholds2004
- Author(s)
  渡辺敬一, 高木俊介
- Journal Title
  
  J. Alg. 282
  
  Pages: 278-297
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] When does the subadditivity theorem for multiplier ideals hold?2004
- Author(s)
  K.-i.Watanabe, S.Takagi
- Journal Title
  
  Trans.Amer.Math.Soc. 356
  
  Pages: 3951-3961
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540005
[Journal Article] On F-pure thresholds,2004
- Author(s)
  S.Takagi, K.Watanabe
- Journal Title
  
  Journal of Algebra, 282
  
  Pages: 278-297
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] When does the subadditivity theorem for multiplier ideals hold?2004
- Author(s)
  渡辺敬一, 高木俊輔
- Journal Title
  
  Trans AMS 356
  
  Pages: 3951-3961
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] The total coordinate ring of a normal projective variety2004
- Author(s)
  J.Elizondo, K.Kurano, K.Watanabe
- Journal Title
  
  J.of Algebra vol.276
  
  Pages: 625-637
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] The total coordinate ring of normal projective variety2004
- Author(s)
  J.Elizondo, K.Kurano, K.Watanabe
- Journal Title
  
  Journal of Algebra 276
  
  Pages: 625-637
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] Minimal relative Hilbert-Kunz multiplicity2004
- Author(s)
  K-i.Watanabe, K.Yoshida
- Journal Title
  
  Illinois Journal of Mathematics 48
  
  Pages: 273-294
- Data Source
  KAKENHI-PROJECT-16540005
[Journal Article] On F-pure thresholds,2004
- Author(s)
  K.Watanabe, S.Takagi
- Journal Title
  
  J.of Algebra 282
  
  Pages: 278-297
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] On F-pure thresholds2004
- Author(s)
  S.Takagi, K.Watanabe
- Journal Title
  
  J.of Algebra vol.282
  
  Pages: 278-297
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] The total coordinate ring of a normal projective variety2004
- Author(s)
  K.-i.Watanabe, J.Elizondo, K.Kurano
- Journal Title
  
  J.Algebra 276
  
  Pages: 625-637
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16540005
[Journal Article] F-thresholds and Bernstein-Sato polynomials2004
- Author(s)
  渡辺敬一, Mustata, 高木俊介
- Journal Title
  
  4ECM Stockholm
  
  Pages: 341-363
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] F-thresholds and Bernstein-Sato polynomials,2004
- Author(s)
  K.Watanabe, M.Mustata, S.Takagi
- Journal Title
  
  4ECM Stockholm
  
  Pages: 341-363
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] Minimal relative Hilbert-kunz multiplicity2004
- Author(s)
  K.Watanabe, K.Yoshida
- Journal Title
  
  Illinois J.Math. 48
  
  Pages: 273-294
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] Minimal relative Hilbert-Kunz multiplicity2004
- Author(s)
  K.-i.Watanabe, K.Yoshida
- Journal Title
  
  Illinois J.Math. 48
  
  Pages: 273-294
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16540005
[Journal Article] On F-pure thresholds2004
- Author(s)
  S.Takagi, K.Watanabe
- Journal Title
  
  J.of Algebra 282
  
  Pages: 278-297
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] Minimal relative Hilbert-Kunz multiplicity2004
- Author(s)
  K-i.Watanabe, K.Yoshida
- Journal Title
  
  Illinois J.Math. 48
  
  Pages: 273-294
- Data Source
  KAKENHI-PROJECT-16540021
[Journal Article] When does the subadditivity theorem for multiplier ideals hold?2004
- Author(s)
  渡辺敬一, 高木俊介
- Journal Title
  
  Trans. AMS 356
  
  Pages: 3951-3961
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] When does the subadditivity for multiplier ideals hold?2004
- Author(s)
  K-i.Watanabe, S.Takagi
- Journal Title
  
  Transactions of American Mathematical Society 356
  
  Pages: 3951-3961
- Data Source
  KAKENHI-PROJECT-16540005
[Journal Article] When does the subadditivity theorem for multiplier ideals hold?2004
- Author(s)
  S.Takagi, K.Watanabe
- Journal Title
  
  Transaction of American Mathematical Society 356
  
  Pages: 3951-3961
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] Minimal relative Hilbert-Kunz multiplicity2004
- Author(s)
  渡辺敬一, 吉田健一
- Journal Title
  
  Illinois Journal of Math. 48
  
  Pages: 625-637
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] Minimal relative Hilbert-Kunz multiplicity2004
- Author(s)
  K.Watanabe, K.Yoshida
- Journal Title
  
  Illinois J.of Mathematics 48
  
  Pages: 273-294
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] The total coordinate ring of a normal projective variety,2004
- Author(s)
  K.Watanabe, Elizondo, K.Kurano
- Journal Title
  
  J.of Algebra vol.276, No.2
  
  Pages: 625-637
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] The total coordinate ring of a normal projective variety2004
- Author(s)
  J.Elizondo, K.Kurano, K.Watanabe
- Journal Title
  
  J.Algebra 276
  
  Pages: 625-637
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540005
[Journal Article] When does the subadditivity theorem for multiplier ideals hold?2004
- Author(s)
  Shunsuke Takagi, Kei-ichi Watanabe
- Journal Title
  
  Trans. Amer. Math. Soc. 356
  
  Pages: 3951-3961
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540021
[Journal Article] The total coordinate ring of a normal projective variety,2004
- Author(s)
  J.Elizondo, K.Kurano, K.Watanabe
- Journal Title
  
  Journal of Algebra, 276
  
  Pages: 625-637
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] The total coordinate ring of a normal projective variety,2004
- Author(s)
  渡辺敬一, Elizondo, 蔵野和彦
- Journal Title
  
  J. of Algebra, 276
  
  Pages: 625-637
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] Minimal relative Hilbert-Kunz multiplicity2004
- Author(s)
  K.-i.Watanabe, K.Yoshida
- Journal Title
  
  Illinois J.Math 48
  
  Pages: 273-294
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540005
[Journal Article] When does the subadditivity theorem for multiplier ideals hold?2004
- Author(s)
  K.Watanabe, S.Takagi
- Journal Title
  
  Trans.AMS vol.356
  
  Pages: 3951-3961
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] Integrally closed ideals in two-dimensional regular local rings are multiplier ideals2003
- Author(s)
  J.Lipman, K.Watanabe
- Journal Title
  
  Math.Reasearch Letters vol.10
  
  Pages: 423-434
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] Integrally closed ideals in two-dimensional regular local rings are multiplier ideals,2003
- Author(s)
  K.Watanabe, Lipman
- Journal Title
  
  Math.Reasearch Letters 10
  
  Pages: 423-434
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] Integrally closed ideals in two-dimensional regular local rings are multiplier ideals2003
- Author(s)
  渡辺敬一, J.Lipman
- Journal Title
  
  Math. Reasearch Letters 10
  
  Pages: 423-434
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] Chains of Integrally Closed Ideals,2003
- Author(s)
  K.Watanabe
- Journal Title
  
  Contem Math. (AMS) 331
  
  Pages: 353-358
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] Integrally closed ideals in two-dimensional regular local rings are multiplier ideals,2003
- Author(s)
  J.Lipman, K.Watanabe
- Journal Title
  
  Math.Reasearch Letters 10
  
  Pages: 423-434
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] Chains of Integrally Closed Ideals2003
- Author(s)
  渡辺敬一
- Journal Title
  
  Contem Math. 331
  
  Pages: 353-358
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-14340005
[Journal Article] F-regular and F-pure rings vs.log terminal and log canonical singularities.2002
- Author(s)
  N.Hara, K.Watanabe
- Journal Title
  
  Journal of Algebraic Geometry vol 11
  
  Pages: 363-392
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] F-rationality of Rees algebras2002
- Author(s)
  N.Hara, K.Watanabe, K.Yoshida
- Journal Title
  
  Journal of Algebra vol 247
  
  Pages: 153-190
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-13440015
[Journal Article] Adjacent integrally closed ideals in 2-dimensional regular local rings,
- Author(s)
  S.Noh, K.Watanabe
- Journal Title
  
  J.of Algebra (印刷中)
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] F-thresholds, tight closure, integral closure, and multiplicity bounds
- Author(s)
  K. i. Watanabe, C. Huneke, M. Mustata, S. Takagi
- Journal Title
  
  Michigan Math. J. (未定)(掲載決定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540051
[Journal Article] Totally reflexive modules constructed from smooth projective curves of genus g 【greater than or equal】 2
- Author(s)
  R.Takahashi, K.Watanabe
- Journal Title
  
  Archiv der Mathematik. To appear
- Data Source
  KAKENHI-PROJECT-17540043
[Journal Article] Adjacent integrally closed ideals in 2-dimensional regular local rings
- Author(s)
  S.NOH, Kei-ichi WATANABE
- Journal Title
  
  J. of Algebra (to appear)(号・巻、発行年、ページ数未定)
- Data Source
  KAKENHI-PROJECT-16540043
[Journal Article] Coefficient ideal of ideals generated by monomials
- Author(s)
  S.Ohnihsi, K.-i.Watanabe
- Journal Title
  
  Communications in Algebra (掲載決定, 巻号未定)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18540051
[Journal Article] Hilbert-Kunz multiplicity of three-dimensional local rings
- Author(s)
  K-i.Watanabe, K.Yoshida
- Journal Title
  
  Nagoya Math.J. (to appear)
- Data Source
  KAKENHI-PROJECT-16540021
[Journal Article] Totally reflexive modulus construsded from projective curves of genus g22
- Author(s)
  渡辺敬一, 高橋良
- Journal Title
  
  Archiv der Mathematik (掲載決定)
- Data Source
  KAKENHI-PROJECT-18340004
[Journal Article] Hilbert-Kunz multiplicity of three-dimensional local rings
- Author(s)
  K-i.Watanabe, K.Yoshida
- Journal Title
  
  Nagoya Mathematical Journal (掲載予定)
- Data Source
  KAKENHI-PROJECT-16540005
[Journal Article] Classification of 2-dimensional normal graded hypersurfaces with a(R) ¥le 6
- Author(s)
  Kei-ichi Watanabe
- Journal Title
  
  Proceedings of the 2012 Conference at IMPA
  
  Volume: (To appear)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Upper bound of multiplicity of F-rational rings and F-pure rings
- Author(s)
  Craig Huneke, . Kei-ichi Watanabe
- Journal Title
  
  Proc. American Mathematical Soc
  
  Volume: (To appear)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-23540059
[Journal Article] Coefficient ideal of ideals generated by monomials
- Author(s)
  S.Ohnishi, K.Watanabe
- Journal Title
  
  Communications in Algebra (To appear)
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-20540050
[Journal Article] Totally reflexive modules constructed from smooth projective curves of genus g≧2
- Author(s)
  R.Takahashi, K.-i.Watanabe
- Journal Title
  
  Arkiv fur Math. (to appear 巻、号、発行年、ページ数未定)
- Data Source
  KAKENHI-PROJECT-18540051
[Presentation] Hilbert-Kunz multiplicities and related topics,2018
- Author(s)
  K. Watanabe
- Organizer
  Colloquium, Institute of mathematics, Hanoi (Vietnam)
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] Homogeneous prime elements of 2-dimensional normal graded rings,2017
- Author(s)
  K. Watanabe
- Organizer
  第39回可換環論シンポジウム，RIMS, 京都大学
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] Normal and core reduction numbers of integrally closed ideals,2017
- Author(s)
  T. Okuma, K. Watanabe and K. Yoshida,
- Organizer
  第39回可換環論シンポジウム，RIMS, 京都大学，
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] Core of p_g-ideals in 2-dimensional normal singularities and a characterization of rational singularities via Core of ideals,2016
- Author(s)
  K. Watanabe
- Organizer
  Math Department Colloquium
- Place of Presentation
  Mumbai (インド)
- Year and Date
  2016-11-04
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] Almost Symmetric Numerical Semigroups2016
- Author(s)
  渡辺　敬一
- Organizer
  研究集会「代数系、論理、言語と計算機科学」
- Place of Presentation
  京都大学数理解析研究所
- Year and Date
  2016-02-16
- Invited
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] Characterization of 2-dimensional rational singularities via core of ideals.2016
- Author(s)
  K. Watanabe
- Organizer
  COMMUTATIVE ALGEBRA AND ITS INTERACTIONS WITH ALGEBRAIC GEOMETRY:
- Place of Presentation
  Ann Arbor (USA)
- Year and Date
  2016-07-10
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] Integrally Closed Ideals of 2-dimensional normal singularities,2015
- Author(s)
  K. Watanabe
- Organizer
  第13回アフィン代数幾何研究集会,
- Place of Presentation
  関西学院大学梅田キャンパス,
- Year and Date
  2015-03-09
- Invited
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] F-thresholds,2015
- Author(s)
  K. Watanabe
- Organizer
  Workshop on Multiplier Ideals, Test Ideals and
- Place of Presentation
  Univ. Politecnica de Catalunya, Barcelona,
- Year and Date
  2015-09-08
- Int'l Joint Research / Invited
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] A characterization of 2-dimensional rational singularities via Core of ideals,2015
- Author(s)
  T. Okuma, K. Watanabe and K. Yoshida,
- Organizer
  第37回可換環論シンポジウム
- Place of Presentation
  倉敷シーサイドホテル
- Year and Date
  2015-11-21
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] p_g-ideals and core of integrally closed ideals in normal surface singularities,2015
- Author(s)
  K. Watanabe
- Organizer
  AMS Summer Institute, Univ. of Utah,
- Place of Presentation
  Univ. of Utah,
- Year and Date
  2015-07-14
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] A classification of integrally closed ideals in 2-dimendional normal singularities and a characterization of2015
- Author(s)
  K. Watanabe
- Organizer
  The 3rd Franco-Japanese-Vietnamese symposium on singularities,
- Place of Presentation
  Math. INstitute, Hanoi, Vietnam
- Year and Date
  2015-12-02
- Int'l Joint Research / Invited
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] Ideal Theory of 2-dimensional normal singularities,2014
- Author(s)
  K. Watanabe
- Organizer
  OSCAR 2
- Place of Presentation
  岡山大学
- Year and Date
  2014-06-09
- Invited
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] Towards the theory of integrally closed ideals of 2-dimensional2014
- Author(s)
  奥間智宏，吉田健一, 渡辺敬一
- Organizer
  第36回可換環論シンポジウム
- Place of Presentation
  湘南国際村
- Year and Date
  2014-11-24
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] Ulrich Ideals,2014
- Author(s)
  K. Watanabe
- Organizer
  International Meeting on numerical semigroups
- Place of Presentation
  Palazzone, Cortona, Italy
- Year and Date
  2014-09-09
- Data Source
  KAKENHI-PROJECT-26400053
[Presentation] Good ideals of 2-dimensional normal singularities2013
- Author(s)
  Kei-ichi Watanabe
- Organizer
  International Conference on Commutative Algebra and its Interaction to Algebraic Geometry and Combinatorics
- Place of Presentation
  Institute of Math., Hanoi
- Year and Date
  2013-12-09
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] Good ideals of 2-dimensional normal singularities2013
- Author(s)
  Kei-ichi Watanabe
- Organizer
  COMMUTATIVE ALGEBRA AND ITS INTERACTION WITH ALGEBRAIC GEOMETRY
- Place of Presentation
  CIRM, France
- Year and Date
  2013-07-10
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] Existence of good ideals in 2-dimensional normal Gorenstein rings2013
- Author(s)
  Kei-ichi Watanabe
- Organizer
  Commutative Algebra Seminar
- Place of Presentation
  MSRI, UC Berkeley
- Year and Date
  2013-03-14
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] On Ulrich ideals and modules, II2012
- Author(s)
  Kei-ichi Watanabe
- Organizer
  12th ALGA meeting
- Place of Presentation
  IMPA, Rio de Janeiro
- Year and Date
  2012-08-16
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] Ulrich modules and Special modules over 2-dimensional rational singularities2012
- Author(s)
  吉田健一・渡辺敬一
- Organizer
  第45回環論および表現論シンポジウム
- Place of Presentation
  信州大学
- Year and Date
  2012-09-08
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] Certain Jet Schemes have Rational Singularities2011
- Author(s)
  Kei-ichi Watanabe
- Organizer
  Midwest Commutative Algebra and Geometry Conference
- Place of Presentation
  Purdue University
- Year and Date
  2011-05-15
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] Certain Jet Schemes have Rational Singularities2011
- Author(s)
  K. Watanabe
- Organizer
  Midwest Commutative Algebra and Geometry Conference,(招待講演)
- Place of Presentation
  Purdue University, USA
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] Upper bound of multiplicity of F-rational and F-pure rings2011
- Author(s)
  渡辺敬一
- Organizer
  第33回可換環論シンポジウム
- Place of Presentation
  浜名湖カリアック
- Year and Date
  2011-11-09
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] The upper bound of multiplicity of F-pure rings and rational singularities2011
- Author(s)
  Kei-ichi Watanabe
- Organizer
  The 7th Japan- Vietnam Joint Seminar on Commutative Algebra
- Place of Presentation
  Quy Nhon University, Vietnam
- Year and Date
  2011-12-13
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] 11/8 トーリック環上の F-thresholds2011
- Author(s)
  吉田健一, 渡辺敬一
- Organizer
  第33回可換環論シンポジウム
- Place of Presentation
  浜名湖カリアック
- Year and Date
  2011-11-08
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] The upper bound of multiplicity of F-pure rings and rational singularities2011
- Author(s)
  K. Watanabe
- Organizer
  The 7th Japan- Vietnam Joint Seminar on Commutative Algebra(招待講演)
- Place of Presentation
  Quy Nhon University, Vietnam
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] Certain Jet Schemes have Rational Singularities2011
- Author(s)
  渡辺敬一
- Organizer
  特異点論とそのひろがり
- Place of Presentation
  京都大学
- Year and Date
  2011-08-24
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] A variant of Wang's Theorem in positive characteristic2010
- Author(s)
  K.Watanabe
- Organizer
  Commutative Algebra and its Interactions with Algebraic Geometry
- Place of Presentation
  C.I.R.M, Luminy (France)
- Year and Date
  2010-11-05
- Data Source
  KAKENHI-PROJECT-22340004
[Presentation] A variant of Wang's Theorem in positive characteristic2010
- Author(s)
  K.Watanabe
- Organizer
  Commutative Algebra and its Interactions with Algebraic Geometry.
- Place of Presentation
  C.I.R.M, Luminy, France
- Year and Date
  2010-11-05
- Data Source
  KAKENHI-PROJECT-20540050
[Presentation] A positive characteristic approach to Wang's theorem2010
- Author(s)
  K.Watanabe, K.Yoshida
- Organizer
  32nd Commutative Algebra Symposium, 6th Japan-Vietnam Joint Seminar on Commutative Algebra
- Place of Presentation
  IPC生産性国際交流センター,葉山
- Year and Date
  2010-12-06
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Some topics on F-thresholds2010
- Author(s)
  K.Watanabe
- Organizer
  Frobenius splitting in algebraic geometry, commutative algebra, and representation theory
- Place of Presentation
  University of Michigan (USA)
- Year and Date
  2010-05-18
- Data Source
  KAKENHI-PROJECT-22340004
[Presentation] Some topics on F-thresholds2010
- Author(s)
  K.Watanabe
- Organizer
  Juergan Herzogを囲む可換代数の集い
- Place of Presentation
  大阪大学
- Year and Date
  2010-01-28
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Some topics on F-thresholds2010
- Author(s)
  K.Watanabe
- Organizer
  Frobenius splitting conferrence
- Place of Presentation
  Michigan University, Ann Arbor
- Year and Date
  2010-05-18
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Some topics on F-thresholds2010
- Author(s)
  K.Watanabe
- Organizer
  Frobenius splitting conference
- Place of Presentation
  Michigan University, Ann Arbor
- Year and Date
  2010-05-18
- Data Source
  KAKENHI-PROJECT-20540050
[Presentation] A positive characteristic approach to Wang's theorem2010
- Author(s)
  K.Watanabe, K.Yoshida
- Organizer
  32nd Commutative Algebra Symposium, 6th Japan-Vietnam Joint Seminar on Commutative Algebra
- Place of Presentation
  葉山
- Year and Date
  2010-12-06
- Data Source
  KAKENHI-PROJECT-22340004
[Presentation] Some topics on F-thresholds2010
- Author(s)
  K.Watanabe
- Organizer
  Workshop on Local Rings and Local Study of Algebraic Varieties
- Place of Presentation
  ICTP Trieste
- Year and Date
  2010-06-07
- Data Source
  KAKENHI-PROJECT-20540050
[Presentation] A positive characteristic approach to Wang's theorem2010
- Author(s)
  K.Yoshida, K.Watanabe
- Organizer
  32nd Commutative Algebra Symposium, 6th Japan-Vietnam Joint Seminar on Commutative Algebra
- Year and Date
  2010-12-06
- Data Source
  KAKENHI-PROJECT-20540050
[Presentation] A variant of Wang's Theorem in positive characteristic2010
- Author(s)
  K.Watanabe
- Organizer
  Commutative Algebra and its Interactions with Algebraic Geometry
- Place of Presentation
  C.I.R.M, Luminy
- Year and Date
  2010-11-05
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Some topics on F-thresholds2010
- Author(s)
  K.Watanabe
- Organizer
  The 5-th Japan-Vietnam Joint Seminar on Commutative Algebra
- Place of Presentation
  Hanoi
- Year and Date
  2010-01-05
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Some topics on F-thresholds2010
- Author(s)
  K.Watanabe
- Organizer
  Workshop on Local Rings and Local Study of Algebraic Varieties
- Place of Presentation
  ICTP Trieste, Itajy
- Year and Date
  2010-06-07
- Data Source
  KAKENHI-PROJECT-22340004
[Presentation] Some topics on F-thresholds2010
- Author(s)
  K.Watanabe
- Organizer
  Workshop on Local Rings and Local Study of Algebraic Varieties
- Place of Presentation
  ICTP Trieste
- Year and Date
  2010-06-07
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Some topics on F-thresholds2010
- Author(s)
  K.Watanabe
- Organizer
  The 5-th Japan-Vietnam Joint Seminar on Commutative Algebra
- Place of Presentation
  Hanoi
- Year and Date
  2010-01-05
- Data Source
  KAKENHI-PROJECT-20540050
[Presentation] A variant of Wang's Theorem in positive characteristic2010
- Author(s)
  Keiichi Watanabe
- Organizer
  Commutative Algebra and its Interactions with Algebraic Geometry
- Place of Presentation
  C.I.R.M., Luminy, France
- Year and Date
  2010-11-05
- Data Source
  KAKENHI-PROJECT-20540050
[Presentation] The a invariants of normal graded Gorenstein rings and varieties with even canonical class2009
- Author(s)
  K.Watanabe
- Organizer
  PASI 2009, Commutative Algebra and its connections to Geometry
- Place of Presentation
  Olinda, Brazil
- Year and Date
  2009-08-14
- Data Source
  KAKENHI-PROJECT-20540050
[Presentation] Hilbert-Kunz multiplicities" (2 talks)2009
- Author(s)
  K.Watanabe
- Organizer
  Mini Workshop of Algebra
- Place of Presentation
  Taiwan National University
- Data Source
  KAKENHI-PROJECT-20540050
[Presentation] The $a$ invariants of normal graded Gorenstein rings and varieties with even canonical class2009
- Author(s)
  K.Watanabe
- Organizer
  第31回可換環論シンポジウム
- Place of Presentation
  アウィーナ大阪
- Year and Date
  2009-11-25
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] The $a$ invariants of normal graded Gorenstein rings and varieties with even canonical class2009
- Author(s)
  K.Watanabe
- Organizer
  日本数学会一般講演
- Place of Presentation
  大阪大学
- Year and Date
  2009-09-26
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] a-invariant of normal graded Gorenstein domains and varieties with even canonical class2009
- Author(s)
  K.Watanabe
- Organizer
  Kommutative Algebra
- Place of Presentation
  Oberwolfach
- Year and Date
  2009-04-24
- Data Source
  KAKENHI-PROJECT-20540050
[Presentation] a-invariant of normal graded Gorenstein domains and varieties with even canonical class2009
- Author(s)
  K.Watanabe
- Organizer
  Kommutative Algebra
- Place of Presentation
  Oberwolfach
- Year and Date
  2009-04-24
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] a-invariant of normal graded Gorenstein domains and varieties with even canonical class2009
- Author(s)
  K.Watanabe
- Organizer
  2009 PRIMA congress
- Place of Presentation
  University of New South Wales, Sydney
- Year and Date
  2009-07-08
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Hilbert-Kunz multiplicities2009
- Author(s)
  K.Watanabe
- Organizer
  Mini Workshop of Algebra
- Place of Presentation
  Taiwan National University
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] The a invariants of normal graded Gorenstein rings and varieties with even canonical class2009
- Author(s)
  K.Watanabe
- Organizer
  PASI 2009, Commutative Algebra and its connections to Geometry
- Place of Presentation
  Olinda, Brazil
- Year and Date
  2009-08-14
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] a-invariant of normal graded Gorenstein domains and varieties with even canonical class2009
- Author(s)
  K.Watanabe
- Organizer
  2009 PRIMA congress
- Place of Presentation
  University of New South Wales, Sydney
- Year and Date
  2009-07-08
- Data Source
  KAKENHI-PROJECT-20540050
[Presentation] a-invariant of normal graded Gorenstein domains and varieties with even canonical class2009
- Author(s)
  K.Watanabe
- Organizer
  Workshop "Kommutative Algebra"
- Place of Presentation
  Oberwolfach 数学研究所
- Year and Date
  2009-04-23
- Data Source
  KAKENHI-PROJECT-20540050
[Presentation] Coefficient ideals of monomial idelas2008
- Author(s)
  K.Watanabe
- Organizer
  第30回可換環論シンポジウム
- Place of Presentation
  唐津
- Year and Date
  2008-11-19
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation]2008
- Author(s)
  K.Watanabe
- Organizer
  Classification of 2-dimensional normal graded hypersurfaces with small a-invariants
- Place of Presentation
  Algebra Workshop, Kansas Univ.
- Year and Date
  2008-07-25
- Data Source
  KAKENHI-PROJECT-20540050
[Presentation] Methods of characteristic $p>0$ in Singularity Theory2008
- Author(s)
  渡辺敬一
- Organizer
  第3回代数・解析・幾何セミナー
- Place of Presentation
  鹿児島大学2/18-21
- Year and Date
  2008-02-18
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Classification of 2-dimensional normal graded hypersurfaces with small a-invariants2008
- Author(s)
  K.Watanabe
- Organizer
  Algebre commutative et ses interactions avec la geometrie algebrique
- Place of Presentation
  C.I.R.M., Luminy, France
- Year and Date
  2008-10-01
- Data Source
  KAKENHI-PROJECT-20540050
[Presentation] F-thresholds,with applications to multiplier ideals,integral closure and multiplicity2008
- Author(s)
  K. Watanabe
- Organizer
  CIMPA Conference on Commutative Algebra
- Place of Presentation
  IIT Bombay,Mumbai,India
- Year and Date
  2008-01-10
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Presentation] Classification of 2-dimensional normal graded hypersurfaces with small a-invariants2008
- Author(s)
  K.Watanabe
- Organizer
  Algebra Workshop
- Place of Presentation
  Kansas Univ.
- Year and Date
  2008-07-25
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] F-thresholds, with applications to multiplier ideals, intgral closure and multiplicity2008
- Author(s)
  K.Watanabe
- Organizer
  Cimpa Conference on Commutative Algebra
- Place of Presentation
  IIT Bombay, Mumbai, India
- Year and Date
  2008-01-10
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Methods of characteristic p>0 in Singularity Theory2008
- Author(s)
  K.Watanabe
- Organizer
  第3回代数・解析・幾何セミナー
- Place of Presentation
  鹿児島大学
- Year and Date
  2008-02-18
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] F-thresholds, with applications to multiplier ideals, intgral closure and multiplicity2008
- Author(s)
  K., Watanabe
- Organizer
  CIMPA Conference on Commutative Algebra
- Place of Presentation
  Bombay, Mumbai, India
- Year and Date
  2008-01-10
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Presentation] Classification of 2-dimensional normal graded hypersurfaces with small a-invariants2008
- Author(s)
  K.Watanabe
- Organizer
  Algebre commutative et ses interactions avec la geometrie algebrique
- Place of Presentation
  C.I.R.M.
- Year and Date
  2008-10-01
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] F-thresholds, with applications to multiplier ideals, integral closure and multiplicity2008
- Author(s)
  渡辺敬一
- Organizer
  CIMPA Conference on Commutative Algebra
- Place of Presentation
  IIT Bombay, Mumbai, India
- Year and Date
  2008-01-10
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Classification of $2$-dimensional normal graded hypersurfaces with $a(R)=1$2007
- Author(s)
  K.Watanabe
- Place of Presentation
  Palo Alto
- Year and Date
  2007-11-22
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] F-thresholds-application to lc thresholds and a conjectur on multiplicity2007
- Author(s)
  K. Watanabe
- Organizer
  Algebraic Geometry and Commutative Algebra Tokyo 2007
- Place of Presentation
  東京大学
- Year and Date
  2007-12-12
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Presentation] Methods of characteristic p>0 in Singularity Theory2007
- Author(s)
  K. i. Watanabe
- Organizer
  Summer School."Characteristic p methods in Algebraic Geometry"
- Place of Presentation
  Drobeta-Turum-Severin; Romania
- Data Source
  KAKENHI-PROJECT-18540051
[Presentation] F-thresholds-application to lc thresholds and a conjecture on multiplicity2007
- Author(s)
  K. Watanabe
- Organizer
  Algebraic Geometry and Commutative Algebra Tokyo 2007,
- Place of Presentation
  東京大学数理科学研究科
- Year and Date
  2007-12-12
- Data Source
  KAKENHI-PROJECT-17540043
[Presentation] F-thresholds-application to lc thresholds and a conjecture on multiplicity2007
- Author(s)
  K., Watanabe
- Organizer
  Algebraic Geometry and Commutative Algebra
- Place of Presentation
  Tokyo University
- Year and Date
  2007-12-12
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Presentation] F-thresholds, tight closure, integral closure and multiplicity bounds (with C. Huneke, M. Mustata, S. Takagi)2007
- Author(s)
  渡辺敬一
- Organizer
  第29回可換環論シンポジウム
- Place of Presentation
  名古屋・池下厚生年金会館
- Year and Date
  2007-11-19
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Methods of Characteristic p>0 in Singularity Theory" Summer School.2007
- Author(s)
  K. i. Watanabe
- Organizer
  Characteristic p methods in Algebraic Geometry
- Place of Presentation
  Drobeta-Turum-Severin; Romania
- Data Source
  KAKENHI-PROJECT-18540051
[Presentation] F-thresholds - application to lc thresholds and a conjecture on multiplicity2007
- Author(s)
  渡辺敬一
- Organizer
  Algebraic Geometry and Commutative Algebra Tokyo 2007
- Place of Presentation
  東京大学
- Year and Date
  2007-12-12
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Methods of characteristic $p>0$ in Singularity Theory2007
- Author(s)
  渡辺敬一
- Organizer
  Summer School, "Characteristic p methods in Algebraic Geometry"(90分, 4回連続講演)
- Place of Presentation
  Drobeta-turum-Severin, Romania
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Ring theoretic properties of F-thresholds2007
- Author(s)
  K.Watanabe
- Organizer
  Hilbert Functions and Syzygies in Commutative Algebra and Combinatorics ; A conference in honor of Juergen Herzog on the occasion of his 65^<th> birthday
- Place of Presentation
  Cortona, Italy
- Year and Date
  2007-09-18
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Ring theoretic properties of F-threshokls2007
- Author(s)
  K. Watanabe
- Organizer
  HILBERT FUNCTINOS AND SYZYGIES IN COMMUTATIVE ALGEBRA AND COMBINATORICS
- Place of Presentation
  CORTONA,Italy
- Year and Date
  2007-09-18
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Presentation] F-thresholds-application to lc thresholds and a conjecture on multiplicity2007
- Author(s)
  K.Watanabe
- Organizer
  Algebraic Geometry and Commutative Algebra Tokyo 2007
- Place of Presentation
  東京大学
- Year and Date
  2007-12-12
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] F-thresholds, tight closure, integral closure and multiplicity bounds2007
- Author(s)
  K.Watanabe, C.Huneke, M.Mustata, S.Takagi
- Organizer
  第29回可換環論シンポジウム
- Place of Presentation
  名古屋・池下厚生年金会館
- Year and Date
  2007-11-19
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Methods of characteristic p>0 in Singularity Theory2007
- Author(s)
  K., Watanabe
- Organizer
  Summer School, "Characteristic p methods in Algebraic Geometry",Drobeta-Turum-Severin
- Place of Presentation
  Romania
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Presentation] Methods of characteristic p>0 in Singularity Theory2007
- Author(s)
  K. Watanabe
- Organizer
  Summer School."Characteristic p methods in Algebraic Geometry"
- Place of Presentation
  Drobeta-Turum-Severin;Romania
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Presentation] Methods of characteristic $p>0$ in Singularity Theory2007
- Author(s)
  K.Watanabe
- Organizer
  Characteristic p methods in Algebraic Geometry
- Place of Presentation
  Drobeta-Turum-Severin ; Romania
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Ring theoretic properties of F-thresholds2007
- Author(s)
  渡辺敬一
- Organizer
  Hilbert functions and Syzygies in Commutative Algebra and Combinatrics: A Conference in honor of Juergen Herzog inthe occasion of his 65th birthday
- Place of Presentation
  Cortona, Italy
- Year and Date
  2007-09-18
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Classification of 2-dimensional normal graded hypersurfaces with a(R)=12007
- Author(s)
  渡辺敬一
- Organizer
  第29回可換環論シンポジウム
- Place of Presentation
  名古屋・池下厚生年金会館
- Year and Date
  2007-11-22
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Presentation] Ring theoretic properties of F-thresholds2006
- Author(s)
  K. Watanabe
- Organizer
  Workshop, "Integral Closure, Multiplier Ideals and Cores"
- Place of Presentation
  American Institute of Mathe matics,Palo Alto,USA
- Year and Date
  2006-12-21
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Presentation] Some characteristic p methods for singularity theory2006
- Author(s)
  K., Watanabe
- Organizer
  Workshop in Commutative Algebra
- Place of Presentation
  Univ. Essen(Germany)
- Year and Date
  2006-11-20
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Presentation] Some Questions on F-thresholds2006
- Author(s)
  K.Watanabe
- Organizer
  Meeting on Commutative Algebra ; Dedicated to the memory of Wilfgang Voge
- Place of Presentation
  Eisenach, Germany
- Year and Date
  2006-11-19
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Some characteristic p methods for singularity theory2006
- Author(s)
  K.Watanabe
- Organizer
  Workshop in Commutative Algebra
- Place of Presentation
  Univ.Essen
- Year and Date
  2006-11-20
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Multiplier ideals and arc spaces2006
- Author(s)
  K.Watanabe
- Place of Presentation
  京都大学数理解析研究所
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Some Questions on F-thresholds2006
- Author(s)
  K. Watanabe
- Organizer
  Meeting on Commutative Algebra;Dedicated to the memory of wilfgang Vogel
- Place of Presentation
  Eisenach,Germany
- Year and Date
  2006-11-19
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Presentation] Some chara-cteistic p methods for singularity theory2006
- Author(s)
  K. Watanabe
- Organizer
  Workshop in Commutative Algebra
- Place of Presentation
  Univ.Essen,Germany
- Year and Date
  2006-11-20
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-17540043
[Presentation] On F-thresholds、京都大学数理研短期共同研究2006
- Author(s)
  渡辺敬一
- Organizer
  京都大学数理研
- Data Source
  KAKENHI-PROJECT-18540051
[Presentation] Ring theoretic properties of F-thresholds, Integral Closure2006
- Author(s)
  K.Watanabe
- Organizer
  Multiplier Ideals and Cores
- Place of Presentation
  American Institute of Mathematics, Palo Alto
- Year and Date
  2006-12-21
- Data Source
  KAKENHI-PROJECT-18340004
[Presentation] Existence of good ideals in 2-dimensional normal Gorenstein rings
- Author(s)
  Kei-ichi Watanabe
- Organizer
  Commutative Algebra Seminar,
- Place of Presentation
  MSRI, UC Berkeley,
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] Good ideals of 2-dimensional normal singularities,
- Author(s)
  K. Watanabe
- Organizer
  COMMUTATIVE ALGEBRA AND ITS INTERACTION WITH ALGEBRAIC GEOMETRY,
- Place of Presentation
  CIRM, France
- Invited
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] Good ideals on 2-dimensional normal singularities,
- Author(s)
  T. Okuma, K. Watanabe, K. Yoshida
- Organizer
  35-th Commutative Algebra Symposium,
- Place of Presentation
  京都大学数理解析研究所
- Data Source
  KAKENHI-PROJECT-23540059
[Presentation] Existence of good ideals in 2-dimensional normal Gorenstein rings
- Author(s)
  K.-i. Watanabe
- Organizer
  Commutative Algebra Seminar
- Place of Presentation
  MSRI, UC Berkeley
- Invited
- Data Source
  KAKENHI-PROJECT-22340004
[Presentation] On Ulrich ideals and modules, II,
- Author(s)
  Kei-ichi Watanabe
- Organizer
  12th ALGA meeting,
- Place of Presentation
  IMPA, Rio de Janeiro,
- Invited
- Data Source
  KAKENHI-PROJECT-23540059

1. 土屋守正 (00188583)

# of Collaborated Projects: 9 results

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2. YOSHIDA Kennichi (80240802)

# of Collaborated Projects: 8 results

# of Collaborated Products: 32 results
3. TOMARI Masataka (60183878)

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4. 成嶋弘 (90056200)

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5. FUKUDA Takuo (00009599)

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6. WATANABE Junzo (40022727)

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7. MATSUURA Yutaka (50096905)

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8. IZUMISAWA Masataka (50108445)

# of Collaborated Projects: 4 results

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9. KURANO Kazuhiko (90205188)

# of Collaborated Projects: 4 results

# of Collaborated Products: 5 results
10. TAKAGI Shunsuke (40380670)

# of Collaborated Projects: 4 results

# of Collaborated Products: 12 results
11. HARA Nobuo (90298167)

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12. 内村桂輔 (20092835)

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13. 原正雄 (10238165)

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14. HASHIMOTO Mitsuyasu (10208465)

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15. YAMAGUCHI Masaru (10056252)

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16. ISHII Shihoko (60202933)

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17. TOMARU Tadashi (70132579)

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18. SUZUKI Masahiko (00171249)

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19. MORI Makoto (60092532)

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20. 永瀬輝男 (90164425)

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21. 桔梗宏孝 (80204824)

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22. MOTEGI Kimihiko (40219978)

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23. ISHIDA Makoto (30124548)

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24. GOTO Shiro (50060091)

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25. FUJITA Takao (40092324)

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26. AKIBA Tomoharu (60027670)

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27. YOSHINO Yuji (00135302)

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28. KURODA Koji (50153416)

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29. SUZUKI Osamu (10096844)

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41. UENO Kenji (40011655)

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42. NISHIDA Kenji (70125392)

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43. YAMAGATA Kunio (60015849)

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44. ITAI Masanori (80266361)

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52. ITO Yukari (70285089)

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53. OKUMA Tomohiro (00300533)

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54. MIWA Megumu (30011521)

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78. 奥間智弘

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Watanabe Keiichi 渡辺 敬一

WATANABE Keiichi 渡辺 敬一

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Commutative Ring Theory of SingularitiesPrincipal Investigator

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Commutative Ring Theory of Singularities of Algebraic VarietiesPrincipal Investigator

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Characteristic p method in singularity theoryPrincipal Investigator

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Singurality Theory and Frobenius MorphismPrincipal Investigator

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整閉イデアルの族の研究Principal Investigator

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Watanabe Keiichi 渡辺敬一

WATANABE Keiichi 渡辺敬一