2020 Fiscal Year Final Research Report
Towards the theory of Algbebraic Symplectic Geometry
| Project/Area Number |
17H02833
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Keywords | シンプレクティック代数多様体 / 錐的シンプレクティック多様体 / ポアソン変形 / 双有理幾何 / シンプレクティック特異点解消 / べき零軌道 |
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| Outline of Final Research Achievements |
Complex algebraic varieties with holomorphic symplectic forms play important roles in algebraic geometry, geometric representation theory and mathematical physics. It is natural to treat those objects admitting singularities. In our research, we have studied "conical symplectic varieties". As concrete results, we first characterized finite coverings of nilpotent orbit closures of a complex semisimple Lie algebra among conical symplectic varieties. Next, we gave an algorithm for constructing a good partial resolution (so called a Q-factorial terminalization) of a conical symplectic variety associated with the universal covering of a nilpotent orbit of a classical Lie algebra. We also counted the number of different Q-factorial terminalizations.
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| Free Research Field |
代数幾何
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| Academic Significance and Societal Importance of the Research Achievements |
本研究の対象である, 錐的シンプレクティック多様体は, 代数幾何と幾何学的表現論の結びつける働きをするものであるが, 代数幾何からアプローチした研究は, ユニークなものである. ここで得られた成果は, 最近, 幾何学的表現論の研究者たちに多く使われるようになった. たとえば, シンプレクティック双対性とよばれる現象が多くの研究者の注目を浴びているが, 研究代表者のおこなった研究は, その中でも重要な働きをしている.
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