Non-commutative crepant resolution, Orbifold cohomology and generalization of the McKay correspondence
Project/Area Number |
23540045
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
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Research Institution | Nagoya University |
Principal Investigator |
Ito Yukari 名古屋大学, 多元数理科学研究科, 准教授 (70285089)
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Co-Investigator(Kenkyū-buntansha) |
伊山 修 名古屋大学, 多元数理科学研究科, 教授 (70347532)
長尾 健太郎 名古屋大学, 多元数理科学研究科, 助教 (10585574)
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Co-Investigator(Renkei-kenkyūsha) |
ISHII Akira 広島大学, 大学院理学研究科, 教授 (10252420)
YOSHIDA Ken-ichi 日本大学, 文理学部, 教授 (80240802)
YASUDA Takehiko 大阪大学, 大学院理学研究科, 准教授 (30507166)
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Research Collaborator |
CRAW Alastair バース大学, 助教授
WEMYSS Michael グラスゴー大学, 教授
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Project Period (FY) |
2011-04-28 – 2017-03-31
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Project Status |
Completed (Fiscal Year 2016)
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Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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Keywords | 商特異点 / 特異点解消 / マッカイ対応 / 非可換クレパント解消 / クイバーの表現 / トーリック幾何学 / クレパント解消 / 三角圏 / McKay対応 / Cohen-Macaulay表現論 / 傾理論 / Auslander-Reiten理論 / 国際研究者交流(イギリス、スウェーデン、他) / 国際研究者交流(イギリス、アメリカ、ドイツ) / 国際情報交換(イギリス、アメリカ、ドイツ) / 国際研究者交流 / 国際情報交流 |
Outline of Final Research Achievements |
Our main aim is to find crepant resolution for quotient singularity and see the McKay correspondence. We have to check the existence of a crepant resolution by construction of a crepant resolution or existenxe of non-commutative crepant resolution. The later one is relatively new idea.The MaKay correspondence is a relation between crepant resolution and group representation.During this research, we found a way to construct a crepant resolution as a moduli space of corresponding representation. Moreover, we showed a generalized McKay correspondence in dimension three as a generalization of special McKay correspondence by using non-commutative corepant resolutions,
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Report
(7 results)
Research Products
(177 results)
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[Journal Article] tau-tilting theory2104
Author(s)
Takahide Adachi, Osamu Iyama, Idun Reiten
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Journal Title
Compos. Math.
Volume: 150
Pages: 415-452
DOI
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Peer Reviewed / Acknowledgement Compliant
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[Presentation] Geigle-Lenzing complete intersections(3回講演)2016
Author(s)
Osamu Iyama
Organizer
Workshop on Weighted Projective Spaces and Representation Theory
Place of Presentation
University of Science and Technology of China, Hefei, China
Year and Date
2016-03-05 – 2016-03-06
Related Report
Int'l Joint Research / Invited
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[Presentation] tau-tilting theory I, II(2回講演)2014
Author(s)
Osamu Iyama
Organizer
Cluster algebras and Representation theory
Place of Presentation
Center for Mathematical Challenges (CMC), KIAS, Seoul, Korea
Year and Date
2014-11-03 – 2014-11-05
Related Report
Invited
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[Presentation] 準傾理論入門2012
Author(s)
Osamu Iyama
Organizer
第2回徳山環論セミナー
Place of Presentation
徳山高専
Year and Date
2012年1月8日
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[Presentation] τ-tilting theory
Author(s)
伊山 修
Organizer
Cluster Algebras in Combinatorics, Algebra, and Geometry
Place of Presentation
Mathematical Sciences Research Instiute
Related Report
Invited
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[Book] 数学辞典2016
Author(s)
伊藤 由佳理ほか
Total Pages
776
Publisher
朝倉書店
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