Study of problems related to derived category of coherent sheaves
| Project/Area Number |
25800017
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 導来圏 / 双有理幾何学 / 半直交分解 / 非可換代数幾何学 / del Pezzo曲面 / Hirzebruch曲面 / モジュライ / 例外対象 / Grothendieck環 / 幾何学的不変式論 / ブラウアー対 / 導来圏(ヨーロッパ) / 非可換代数幾何学(ヨーロッパ) / ブラウアー対(ヨーロッパ・北米・オーストラリア) / 箙 / 非可換代数多様体 |
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| Outline of Final Research Achievements |
With Kotaro Kawatani, we studied the relationship between the semi-orthogonal decompositions of the derived category of coherent sheaves and the canonical linear system. We obtained some results in this direction. Also with Hokuto Uehara, we identified the structure of the exceptional sheaves on the Hirzebruch surface of degree 2.
Concerning noncommutative algebraic geometry, with Tarig Abdelgadir and Kazushi Ueda, we introduced a certain construction of compactified moduli spaces of noncommutative algebraic varieties and studied their structures for the case of noncommutative del Pezzo surfaces. Also with Taro Sano, we studied the noncommutative rigidity of the moduli stack of stable pointed curves.
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Report
(5 results)
Research Products
(37 results)
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[Presentation] Noncommutative Hirzebruch surfaces2016
Author(s)
Shinnosuke Okawa
Organizer
Categorical and analytic invariants in Algebraic geometry 3
Place of Presentation
Higher School of Economics, Russia
Year and Date
2016-09-12
Related Report
Int'l Joint Research / Invited
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[Presentation] Noncommutative Hirzebruch surfaces2016
Author(s)
Shinnosuke Okawa
Organizer
School and Workshop on Homological Methods in Algebra and Geometry
Place of Presentation
African Institute for Mathematical Sciences Ghana, Ghana
Year and Date
2016-08-01
Related Report
Int'l Joint Research / Invited
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[Presentation] On noncommutative Hirzebruch surfaces2016
Author(s)
Shinnosuke Okawa
Organizer
Non-commutative crepant resolutions, Ulrich Modules and generalizations of the McKay correspondence
Place of Presentation
京都大学数理解析研究所
Year and Date
2016-06-13
Related Report
Int'l Joint Research / Invited
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