2016 Fiscal Year Final Research Report
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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| Keywords | シンプレクティック特異点 / ポアソン変形 / 双有理幾何 |
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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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| Free Research Field |
代数幾何, 複素シンプレクテイック幾何
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