| Co-Investigator(Kenkyū-buntansha) |
戸田 幸伸 東京大学, カブリ数物連携宇宙研究機構, 教授 (20503882)
中村 勇哉 東京大学, 大学院数理科学研究科, 助教 (20780034)
高木 俊輔 東京大学, 大学院数理科学研究科, 教授 (40380670)
大川 新之介 大阪大学, 理学研究科, 准教授 (60646909)
權業 善範 東京大学, 大学院数理科学研究科, 准教授 (70634210)
小木曽 啓示 東京大学, 大学院数理科学研究科, 教授 (40224133)
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| Budget Amount *help |
¥46,020,000 (Direct Cost: ¥35,400,000、Indirect Cost: ¥10,620,000)
Fiscal Year 2020: ¥8,060,000 (Direct Cost: ¥6,200,000、Indirect Cost: ¥1,860,000)
Fiscal Year 2019: ¥8,840,000 (Direct Cost: ¥6,800,000、Indirect Cost: ¥2,040,000)
Fiscal Year 2018: ¥8,840,000 (Direct Cost: ¥6,800,000、Indirect Cost: ¥2,040,000)
Fiscal Year 2017: ¥8,840,000 (Direct Cost: ¥6,800,000、Indirect Cost: ¥2,040,000)
Fiscal Year 2016: ¥11,440,000 (Direct Cost: ¥8,800,000、Indirect Cost: ¥2,640,000)
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| Outline of Final Research Achievements |
The theory of non-commutative deformations and its applications to birational geometry were the main research topics. For deformations of coherent sheaves or perverse coherent sheaves, it is natural to consider non-commutative rings as parameter rings because they are described by DG algebras. There are more non-commutative deformations than commutative ones and we can study deeper structure of algebraic varieties. In this study, we develop a general theory of multi-pointed non-commutative deformations and describe semi-universal deformations of simple collections or partial simple collections. As an application, we studied semi-orthogonal decompositions of derived categories of algebraic varieties that have singularities. We constructed locally free sheaves from divisorial sheaves on algebraic surfaces using non-commutative deformations, and constructed semi-orthogonal decompositions for some singular rational surfaces, and also for some three-dimensional varieties.
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