Symplectic singularities
Symplectic singularities
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DOI：
10.1007/s002229900043
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发表时间：
2000-03-01
影响因子：
3.1
通讯作者：
Beauville, A
中科院分区：
文献类型：
--
作者：
Beauville, A
我们讨论一类特殊的理性Gorenstein奇点，我们称之为辛。一个正规簇V有辛奇点，如果它的光滑部分带有一个闭辛2-形式，其在任何分解X -> V上的拉回延伸到X上的一个全纯2-形式。我们的主要结果是具有光滑射影切锥的孤立辛奇点的分类。它们与简单复李代数一一对应：李代数g对应于g中最小（非零）幂零伴随轨道的闭包在0处的奇点。
We discuss a particular class of rational Gorenstein singularities, which we call symplectic. A normal variety V has symplectic singularities if its smooth part carries a closed symplectic 2-form whose pull-back in any resolution X --> V extends to a holomorphic 2-form on X . Our main result is the classification of isolated symplectic singularities with smooth projective tangent cone. They are in one-to-one correspondence with simple complex Lie algebras: to a Lie algebra g corresponds the singularity at 0 of the closure of the minimal (nonzero) nilpotent adjoint orbit in g .