Geometry of quiver varieties and representation theory
Project/Area Number |
19340006
|
Research Category |
Grant-in-Aid for Scientific Research (B)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Kyoto University |
Principal Investigator |
NAKAJIMA Hiraku Kyoto University, 数理解析研究所, 教授 (00201666)
|
Co-Investigator(Kenkyū-buntansha) |
ISHII Akira 広島大学, 大学院・理学研究科, 准教 (10252420)
YOSHIOKA Kota 神戸大学, 大学院・理学研究科, 教授 (40274047)
|
Project Period (FY) |
2007 – 2010
|
Project Status |
Completed (Fiscal Year 2010)
|
Budget Amount *help |
¥8,190,000 (Direct Cost: ¥6,300,000、Indirect Cost: ¥1,890,000)
Fiscal Year 2010: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2009: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2008: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2007: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
|
Keywords | インスタントン / ドナルドソン不変量 / 偏屈連接層 / 壁越え公式 / 量子アファイン展開環 / 箙多様体 / クラスター代数 / インスタントンの数え上げ / 壁越え / モジュライ空間 |
Research Abstract |
Consider the blowup of a complex algebraic surface at a point. Together with Yoshioka, I introduced an abelian category in the derived category of coherent sheaves, called the category of perverse coherent sheaves, and study its moduli spaces. As an application, further with Gottsche, I proved Witten's conjecture equating Donaldson invariants and Seiberg-Witten invariants for complex surfaces.
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Report
(6 results)
Research Products
(49 results)
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[Presentation] Quiver varieties and cluster algebras2009
Author(s)
Hiraku Nakajima
Organizer
Summer School and Conference in Geometric Representation Theory and Extended Affine Lie Algebras
Place of Presentation
University of Ottawa, Ontario, Canada
Year and Date
2009-07-01
Related Report
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