Research on the McKay correspondence and derived categories

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540041
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Hiroshima University
• Principal Investigator: ISHII Akira 広島大学, 理学(系)研究科(研究院), 教授 (10252420)
• 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)
• Project Period (FY): 2012-04-01 – 2015-03-31
• 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

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.

Free Research Field

代数幾何学