Equivalence of symplectic singularities
Equivalence of symplectic singularities
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DOI：
10.1215/21562261-2081270
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发表时间：
2011-02
影响因子：
0.6
通讯作者：
Y. Namikawa
中科院分区：
文献类型：
--
作者：
Y. Namikawa
设X是仿射正态簇，C^*-作用只有正权。设X_{reg}具有权为L的辛2-形式w，我们证明了当L不为零时，w是权为L直到C^*-等变自同构的唯一辛2-形式，当$L=0$时，我们有一个反例.在本文的后半部分，我们将一个射影簇P(X)联系到X上，并证明了P(X)有一个接触或双波结构。此外，当X具有正则奇点时，接触结构在小变形下是刚性的。利用P(X)上的接触结构，我们讨论了(X，w)至常数的等价问题。在大多数例子中，辛结构被证明是唯一的，直到恒定，只有极少数例外。
Let X be an affine normal variety with a C^*-action having only positive weights. Assume that X_{reg} has a symplectic 2-form w of weight l. We prove that, when l is not zero, the w is a unique symplectic 2-form of weight l up to C^*-equivariant automorphism When $l = 0$, we have a counter-example to this statement. In the latter half of the article, we associate to X a projective variety P(X) and prove that P(X) has a contact orbifold structure. Moreover, when X has canonical singularities, the contact orbifold structure is rigid under a small deformation. By using the contact structure on P(X), we discuss the equivalence problem for (X, w) up to contant. In most examples the symplectic structures turn out to be unique up to constant with very few exceptions.