| Project/Area Number |
21840030
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
OKADA So Kyoto University, 数理解析研究所, 特定研究員(グローバルCOE) (50547015)
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| Project Period (FY) |
2009 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥2,223,000 (Direct Cost: ¥1,710,000、Indirect Cost: ¥513,000)
Fiscal Year 2010: ¥1,066,000 (Direct Cost: ¥820,000、Indirect Cost: ¥246,000)
Fiscal Year 2009: ¥1,157,000 (Direct Cost: ¥890,000、Indirect Cost: ¥267,000)
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| Keywords | ホモロジカルミラー対称性 / 導来圏 / 安定性条件 / 保型形式 |
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| Research Abstract |
We study derived categories, using stability conditions. In particular, we deal with homological mirror symmetry for Fermat polynomials. From studies on string theory, Kontsevich proposes the symmetry as equivalence of derived categories of coherent sheaves and Lagrangians. We give equivalence of derived categories of equivariant coherent sheaves and Fukaya-Seidel categories, and discuss categorical Pontryagin dualities. We give quiver descriptions of Fukaya-Seidel categories and discuss stability conditions. We study modularity, counting rigid semistable objects.
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