2018 Fiscal Year Final Research Report
Singularities and derived catetories
| Project/Area Number |
15K04819
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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 | Nagoya University (2018)
Hiroshima University (2015-2017) |
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Principal Investigator |
Ishii Akira 名古屋大学, 多元数理科学研究科, 教授 (10252420)
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| Research Collaborator |
Nakamura Iku
Ueda Kazushi
Álvaro Nolla
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Keywords | McKay対応 / モジュライ空間 / ダイマー模型 |
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| Outline of Final Research Achievements |
(1) We studied some globalisation of the so-called special McKay correspondence for a two-dimensional quotient singularity with Iku Nakamura and obtained a description of it.
(2) For a two-dimensional quotient singularity, we characterized those resolutions dominated by the so-called maximal resolution as the moduli spaces of G-constellations.
(3) We studied dimer models with group actions with Alvaro Nolla and Kazushi Ueda and constructed non-commutative crepant resolutions of the quotient of an affine topic variety by the symmetry of a lattice polygon.
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| Free Research Field |
代数幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
(1) これまで知られていたことに対し，より深い洞察を与えることができた．
(2) これまで違う文脈で出てきた二つの概念を結びつけるとともに，導来圏に関する一般的な予想とよく適合する結果である．
(3) 群の作用を考えることで，これまでの結果を一般化するとともに，新しい例の構成に成功した．
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