2010 Fiscal Year Final Research Report
Geometry of quiver varieties and representation theory
| Project/Area Number |
19340006
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
NAKAJIMA Hiraku Kyoto University, 数理解析研究所, 教授 (00201666)
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| 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)
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| Project Period (FY) |
2007 – 2010
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| 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 |
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| 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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