Yamaki Kazuhiko 山木壱彦

… Alternative Names

YAMAKI Kazuhiko 山木壱彦

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Researcher Number	80402973
Other IDs
Affiliation (Current)	2025: 東北大学, 理学研究科, 教授
Affiliation (based on the past Project Information) *help	2024: 東北大学, 理学研究科, 教授 2021 – 2023: 筑波大学, 数理物質系, 教授 2014 – 2020: 京都大学, 国際高等教育院, 准教授 2010 – 2012: 京都大学, 高等教育研究開発推進機構, 准教授 2009: Kyoto University, 工学研究科, 講師
Review Section/Research Field	Principal Investigator Basic Section 11010:Algebra-related / Algebra / Basic Section 11010:Algebra-related Except Principal Investigator Basic Section 11010:Algebra-related
Keywords	Principal Investigator 非アルキメデス的幾何 / トロピカル化 / トロピカル幾何 / ベルコビッチ空間 / アラケロフ幾何 / ハイブリッド空間 / 骨格 / ベルコビッチ解析空間 / 忠実トロピカル化 / 幾何的ボゴモロフ予想 … More / 高さ / ボゴモロフ予想 / smooth tropicalizations / toric ranks / Tamagawa numbers / Modular curves / 凸幾何 / テータ函数 / スケルトン / 国際研究者交流（フランス、イタリア） / 線形系 / 極限トロピカル化 / トロピカル化写像 / Gross-Schoen輪体 / グラフ / 有理点 / 標準測度 / 代数幾何 … More Except Principal Investigator 不分岐コホモロジー群 / 双有理不変量 / 有理性問題 / ハッセ・ノルム原理 / 代数的トーラス / Berkovich解析空間 / 解析的捩率 / 非アルキメデス幾何 / 代数・数論力学系 / トロピカル幾何 / Berkovich 解析空間 Less

Number theory and algebraic geometry and computer mathematics - New developments on rationality problems for algebraic varieties -
- Principal Investigator
  
  星明考
- Project Period (FY)
  2024 – 2026
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Niigata University
トロピカル滑らかさと忠実性Principal Investigator
- Principal Investigator
  
  山木壱彦
- Project Period (FY)
  2023 – 2025
- Research Category
  
  Grant-in-Aid for JSPS Fellows
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  University of Tsukuba
ハイブリッド空間の研究と算術への応用Principal Investigator
- Principal Investigator
  
  山木壱彦
- Project Period (FY)
  2023 – 2026
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  University of Tsukuba
Fusion of nonarchimedean geometry and Arakelov geometryPrincipal Investigator
- Principal Investigator
  
  Yamaki Kazuhiko
- Project Period (FY)
  2018 – 2023
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  University of Tsukuba
  Kyoto University
Berkovich analytic space, tropical geometry, and algebraic/arithmetic dynamics
- Principal Investigator
  
  Kawaguchi Shu
- Project Period (FY)
  2018 – 2022
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Review Section
  
  Basic Section 11010:Algebra-related
- Research Institution
  Doshisha University
Nonarchimedean geometry and its application to arithmetic of algebraic varietiesPrincipal Investigator
- Principal Investigator
  
  Yamaki Kazuhiko
- Project Period (FY)
  2014 – 2017
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Algebra
- Research Institution
  Kyoto University
Research on heights on algebraic varietiesfrom the viewpoint of Arakelov geometry and its applicationPrincipal Investigator
- Principal Investigator
  
  YAMAKI Kazuhiko
- Project Period (FY)
  2009 – 2012
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Algebra
- Research Institution
  Kyoto University

All 2023 2022 2021 2019 2018 2017 2016 2015 2014 2012 2010 2009

All Journal Article Presentation

[Journal Article] Effective faithful tropicalizations associated to linear systems on curves2021
- Author(s)
  Kawaguchi Shu、Yamaki Kazuhiko
- Journal Title
  
  Memoirs of the American Mathematical Society
  
  Volume: 270 Issue: 1323 Pages: 1-110
- DOI
  10.1090/memo/1323
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18H01114
[Journal Article] Effective Faithful Tropicalizations Associated to Adjoint Linear Systems2018
- Author(s)
  Kawaguchi Shu、Yamaki Kazuhiko
- Journal Title
  
  International Mathematics Research Notices
  
  Volume: - Issue: 19 Pages: 6089-6112
- DOI
  10.1093/imrn/rnx302
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26800012, KAKENHI-PROJECT-18H01114
[Journal Article] Geometric Bogomolov conjecture for nowhere degenerate abelian varieties of dimension $5$ with trivial trace2017
- Author(s)
  Yamaki Kazuhiko
- Journal Title
  
  Mathematical Research Letters
  
  Volume: 24 Issue: 5 Pages: 1555-1563
- DOI
  10.4310/mrl.2017.v24.n5.a10
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26800012
[Journal Article] Survey on the geometric Bogomolov conjecture2017
- Author(s)
  Yamaki Kazuhiko
- Journal Title
  
  Publications math?matiques de Besan?on
  
  Volume: - Pages: 137-193
- DOI
  10.5802/pmb.19
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-26800012
[Journal Article] Algebraic rank on hyperelliptic graphs and graphs of genus 32016
- Author(s)
  Shu Kawaguchi, Kazuhiko Yamaki
- Journal Title
  
  Kyoto Journal of Mathematics
  
  Volume: 56 Issue: 1 Pages: 177-196
- DOI
  10.1215/21562261-3445192
- Peer Reviewed / Acknowledgement Compliant
- Data Source
  KAKENHI-PROJECT-26800012, KAKENHI-PROJECT-15K04817
[Journal Article] Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration (with an appendix by Walter Gubler: the minimal dimension of a canonical measure)2012
- Author(s)
  Kazuhiko Yamaki
- Journal Title
  
  manuscripta mathematica (2012 online)
  
  Volume: 142 Issue: 3-4 Pages: 273-306
- DOI
  10.1007/s00229-012-0599-1
- Year and Date
  2012-11-29
- Data Source
  KAKENHI-PROJECT-21740012
[Journal Article] Graph invariants and the positivity of the height of the Gross-Schoencycle for some curves2010
- Author(s)
  山木壱彦
- Journal Title
  
  manuscripta mathematica 131
  
  Pages: 149177-149177
- NAID
  120002511352
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740012
[Journal Article] Graph invariants and the positivity of the height of the Gross-Schoen cycle for some curves2010
- Author(s)
  Kazuhiko Yamaki
- Journal Title
  
  Manuscripta mathematica
  
  Volume: 131巻 Pages: 149-177
- NAID
  120002511352
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-21740012
[Presentation] アーベル多様体の骨格の忠実トロピカル化2023
- Author(s)
  山木　壱彦
- Organizer
  第30回代数曲面ワークショップ
- Invited
- Data Source
  KAKENHI-PROJECT-18K03211
[Presentation] アーベル多様体の骨格の忠実トロピカル化2023
- Author(s)
  山木　壱彦
- Organizer
  代数幾何学城崎シンポジウム2023
- Invited
- Data Source
  KAKENHI-PROJECT-23K03046
[Presentation] 多面体的多様体の因子に付随した忠実埋め込み2022
- Author(s)
  山木壱彦
- Organizer
  第４回トロピカル幾何ワークショップ
- Invited
- Data Source
  KAKENHI-PROJECT-18K03211
[Presentation] 幾何的ボゴモロフ予想の進展2021
- Author(s)
  山木　壱彦
- Organizer
  日本数学会
- Invited
- Data Source
  KAKENHI-PROJECT-18K03211
[Presentation] Progress in the geometric Bogomolov conjecture2021
- Author(s)
  Kazuhiko Yamaki
- Organizer
  Recent Developments in Algebraic Geometry, Arithmetic and Dynamics Part 1
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03211
[Presentation] Ample divisors on tropical varieties2019
- Author(s)
  Kazuhiko Yamaki
- Organizer
  Workshop "Regensburg days on non-archimedean geometry"
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03211
[Presentation] Ample divisors on tropical toric varieties2019
- Author(s)
  Kazuhiko Yamaki
- Organizer
  The 14th Kagoshima Algebra-Analysis-Geometry Seminar --- On the occasion of Prof. Yokura's retirement ---
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K03211
[Presentation] 代数多様体の非アルキメデス的解析幾何とトロピカル化2018
- Author(s)
  山木　壱彦
- Organizer
  野田代数幾何学シンポジウム 2018
- Invited
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] Effective faithful tropicalizations associated to adjoint linear systems2018
- Author(s)
  Kazuhiko Yamaki
- Organizer
  Workshop: Log geometry, degenerations and related topics.
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] ベルコビッチ曲線の直線束に付随したトロピカル化2017
- Author(s)
  山木壱彦
- Organizer
  野田代数幾何学シンポジウム 2017
- Place of Presentation
  東京理科大学理工学部（千葉県野田市）
- Invited
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] Strict supports of canonical measures and applications to the geometric Bogomolov conjecture2017
- Author(s)
  Kazuhiko Yamaki
- Organizer
  Arakelov Geometry and diophantine applications
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] 直線束を使った忠実トロピカル化：次元が高い場合でも言えること2017
- Author(s)
  山木　壱彦
- Organizer
  第５回 K3曲面・エンリケス曲面ワークショップ
- Invited
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] 曲線に対する幾何的ボゴモロフ予想の証明---代数幾何的な議論を中心に2017
- Author(s)
  山木　壱彦
- Organizer
  九大代数幾何セミナー
- Invited
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] 幾何的ボゴモロフ予想について2016
- Author(s)
  山木壱彦
- Organizer
  第２１１回数理情報科学談話会
- Place of Presentation
  鹿児島大学理学部
- Year and Date
  2016-03-23
- Invited
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] Non-density of small points on divisors on abelian varieties and the Bogomolov conjecture2016
- Author(s)
  Kazuhiko Yamaki
- Organizer
  special events (higher invariants)
- Place of Presentation
  University of Regensburg（ドイツ国レーゲンスブルク市）
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] Effective faithful tropicalizations associated to linear systems on curves2016
- Author(s)
  山木　壱彦
- Organizer
  代数幾何学城崎シンポジウム2016
- Place of Presentation
  城崎国際アートセンター（兵庫県豊岡市）
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] Effective faithful tropicalizations associated to linear systems on curves2016
- Author(s)
  Kazuhiko Yamaki
- Organizer
  Tropical Geometry and Related Topics
- Place of Presentation
  Department of Mathematics, Kyoto University
- Year and Date
  2016-03-09
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] 幾何的ボゴモロフ予想について2016
- Author(s)
  山木壱彦
- Organizer
  東北大代数セミナー
- Place of Presentation
  東北大学理学部（宮城県仙台市）
- Invited
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] Introduction to Berkovich spaces and skeleta2016
- Author(s)
  Kazuhiko Yamaki
- Organizer
  Tropical Geometry and Related Topics
- Place of Presentation
  Department of Mathematics, Kyoto University
- Year and Date
  2016-03-08
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] The geometric Bogomolov conjecture for curves2016
- Author(s)
  Kazuhiko Yamaki
- Organizer
  Arithmetic and Algebraic Geometry 2016
- Place of Presentation
  Graduate School of Mathematical Sciences The University of Tokyo
- Year and Date
  2016-01-25
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] 函数体上の曲線に対するボゴモロフ予想2015
- Author(s)
  山木壱彦
- Organizer
  第３回K3曲面・エンリケス曲面ワークショップ
- Place of Presentation
  北海道教育大学　札幌駅前サテライト
- Year and Date
  2015-08-17
- Invited
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] Recent progress in the geometric Bogomolov conjecture2015
- Author(s)
  Kazuhiko Yamaki
- Organizer
  Non archimedean analytic Geometry: Theory and Practice
- Place of Presentation
  Maison de la Culture, Papeete
- Year and Date
  2015-08-28
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] Bogomolov conjecture for curves over any function field2015
- Author(s)
  Kazuhiko Yamaki
- Organizer
  Intercity Seminar on Arakelov Geometry
- Place of Presentation
  Kyoto University (Lecture Room 110, Dept. Math.)
- Year and Date
  2015-09-06
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] 代数曲線の因子の階数とグラフの因子の階数（川口周氏との共同研究）2014
- Author(s)
  山木壱彦
- Organizer
  研究集会　射影多様体の幾何とその周辺 2014
- Place of Presentation
  高知大学理学部
- Year and Date
  2014-11-02
- Invited
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] Strict supports of canonical measures and applications to the geometric Bogomolov conjecture2014
- Author(s)
  Kazuhiko Yamaki
- Organizer
  Special week: Berkovich spaces and applications
- Place of Presentation
  Strasbourg University
- Year and Date
  2014-06-27
- Invited
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] 幾何的ボゴモロフ予想について2014
- Author(s)
  山木　壱彦
- Organizer
  研究集会「代数多様体とその周辺」
- Place of Presentation
  琉球大学理学部
- Year and Date
  2014-09-30
- Invited
- Data Source
  KAKENHI-PROJECT-26800012
[Presentation] Strict supports of canonical measures and applications to the geometric Bogomolov conjecture2012
- Author(s)
  山木　壱彦
- Organizer
  Paris-Barcelona-Kyoto Seminar on Arakelov Geometry
- Place of Presentation
  京都大学
- Invited
- Data Source
  KAKENHI-PROJECT-21740012
[Presentation] Strict supports of canonical measures and applications to the geometric Bogomolov conjecture2012
- Author(s)
  山木壱彦 ,発表題目
- Organizer
  Paris-Barcelona-Kyoto seminar in Arakelov geometry
- Place of Presentation
  京都大学
- Year and Date
  2012-09-21
- Data Source
  KAKENHI-PROJECT-21740012
[Presentation] Recent development on the geometric Bogomolov conjecture2010
- Author(s)
  山木壱彦
- Organizer
  Torsion of Abelian Schemes and Rational Points on Moduli Spaces
- Place of Presentation
  ボルドー第一大学(フランス)
- Year and Date
  2010-01-25
- Data Source
  KAKENHI-PROJECT-21740012
[Presentation] Recent development on the geometric Bogomolov conjecture2010
- Author(s)
  山木壱彦
- Organizer
  Torsion on abelian schemes and rational points on moduli spaces
- Place of Presentation
  Institut de Mathematiques de Bordeaux
- Year and Date
  2010-01-25
- Data Source
  KAKENHI-PROJECT-21740012
[Presentation] Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration2010
- Author(s)
  山木壱彦
- Organizer
  Paris-Barcelona-Kyoto seminar in Arakelov geometry
- Place of Presentation
  京都大学
- Year and Date
  2010-09-21
- Data Source
  KAKENHI-PROJECT-21740012
[Presentation] グラフ不変量と曲線上の高さに関する話題2009
- Author(s)
  山木壱彦
- Organizer
  代数幾何の関連する諸分野
- Place of Presentation
  北海道大学理学部3号館
- Year and Date
  2009-09-04
- Data Source
  KAKENHI-PROJECT-21740012

1. Kawaguchi Shu (20324600)

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2. 星明考 (50434262)

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3. 山崎愛一 (10283590)

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4. 木田雅成 (20272057)

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5. 岡田拓三 (20547012)

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6. 安田健彦 (30507166)

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7. 下元数馬 (70588780)

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8. 小島秀雄 (90332824)

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9. 橋詰健太 (40934211)

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10. HELMINCK PAUL

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Yamaki Kazuhiko 山木 壱彦

YAMAKI Kazuhiko 山木 壱彦

Research Projects

Research Products

Co-Researchers

Number theory and algebraic geometry and computer mathematics - New developments on rationality problems for algebraic varieties -

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

トロピカル滑らかさと忠実性Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

ハイブリッド空間の研究と算術への応用Principal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Fusion of nonarchimedean geometry and Arakelov geometryPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Berkovich analytic space, tropical geometry, and algebraic/arithmetic dynamics

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Nonarchimedean geometry and its application to arithmetic of algebraic varietiesPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Research on heights on algebraic varietiesfrom the viewpoint of Arakelov geometry and its applicationPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

[Journal Article] Effective faithful tropicalizations associated to linear systems on curves2021

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Effective Faithful Tropicalizations Associated to Adjoint Linear Systems2018

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Geometric Bogomolov conjecture for nowhere degenerate abelian varieties of dimension $5$ with trivial trace2017

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Survey on the geometric Bogomolov conjecture2017

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Algebraic rank on hyperelliptic graphs and graphs of genus 32016

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration (with an appendix by Walter Gubler: the minimal dimension of a canonical measure)2012

Author(s)

Journal Title

DOI

Year and Date

Data Source

[Journal Article] Graph invariants and the positivity of the height of the Gross-Schoencycle for some curves2010

Author(s)

Yamaki Kazuhiko 山木壱彦

YAMAKI Kazuhiko 山木壱彦