2011 Fiscal Year Final Research Report
Moduli spaces and derived categories
| Project/Area Number |
21540039
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Hiroshima University |
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Principal Investigator |
ISHII Akira 広島大学, 大学院・理学研究科, 准教授 (10252420)
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| Co-Investigator(Kenkyū-buntansha) |
SHIMADA Ichiro 広島大学, 大学院・理学研究科, 教授 (10235616)
SHUN-ICHI Kimura 広島大学, 大学院・理学研究科, 教授 (10284150)
HIDEYASU Sumihiro 広島大学, 大学院・理学研究科, 名誉教授 (60068129)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 導来圏 / McKay対応 / ダイマー模型 / ミラー対称性 / ヒルベルトスキーム |
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| Research Abstract |
We determined the consistency condition for dimer models which ensures the derived equivalence between the quiver with relations and the 3-dimensional Gorenstein affine toric variety associated to it. We constructed a full strong exceptional collection consisting of line bundles on a 2-dimensional toric weak Fano stack. We proved that the remaining component in the special McKay correspondence is generated by an exceptional collection. We obtained a certain kind of description of the derived category of a Fermat variety. We obtained some results on iterated G-Hilbert schemes.
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