2016 Fiscal Year Final Research Report
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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| 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 |
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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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| Free Research Field |
代数幾何学
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