Symplectic Algebraic Geometry
| Project/Area Number |
25287003
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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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) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥7,410,000 (Direct Cost: ¥5,700,000、Indirect Cost: ¥1,710,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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| Keywords | シンプレクティック特異点 / ポアソン変形 / 双有理幾何 / ポアソン幾何 / 複素シンプレクティック幾何 / べき零軌道 / 複素接触幾何 / 複素シンプレクティック多様体 / 複素接触多様体 |
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| Outline of Final Research Achievements |
An algebraic variety often has a singularity. Among them an important role plays a singularity that has a symplectic structure.We call it a symplectic singularity. A symplectic singularity is an important object which is closely related with hyperkahler geometry and geometric representation theory.In most cases a symplectic singularity shows up with a 1-dimensional torus action. Such a singularity is particularly called a conical symplectic singularity. We discovered that there is a close relationship between the universal Poisson deformation of a conical symplectic singularity and the birational geometry of its crepant resolution. We also started classifing conical symplectic singularities. Our main results contain a certain finiteness theorem for symplectic singularities and the characterization of a nilpotent orbit closure of complex semisimple Lie algebra.
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Report
(5 results)
Research Products
(28 results)
