Research on the McKay correspondence and derived categories
| Project/Area Number |
24540041
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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, 理学(系)研究科(研究院), 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)
KIMURA Shun-ichi 広島大学, 大学院理学研究科, 教授 (10284150)
SUMIHIRO Hideyasu 広島大学, 大学院理学研究科, 名誉教授 (60068129)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | マッカイ対応 / ダイマー模型 / クレパント解消 / 非可換クレパント解消 / 国際研究者交流（スペイン） / モジュライ空間 / 導来圏 |
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| Outline of Final Research Achievements |
We considered problems on dimer models, which are certain bipartite graphs on the 2-torus. We first proved that a non-degenerate dimer model can be made consistent without changing its characteristic polygon. For a dimer model with a finite group action, we defineded a natural action of the same group on the associated 3-dimensional toric variety in such a way that the action on the canonical sheaf is trivial. Given a Gorenstein affine toric 3-fold with a gout action, we considered the problem whether there exists an consistent dimer model with a group action corresponding to it. In many cases, we obtained an affirmative answer.
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Report
(4 results)
Research Products
(12 results)
