2010 Fiscal Year Final Research Report
Study on derived categories
| 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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| 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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