Poisson deformations of affine symplectic varieties II
Abstract
This is a continuation of math.AG/0609741. Let Y be an affine symplectic variety with a C^*-action with positive weights, and let \pi: X -> Y be its crepant resolution. Then \pi induces a natural map PDef(X) -> PDef(Y) of Kuranishi spaces for the Poisson deformations of X and Y. In the Part I, we proved that PDef(X) and PDef(Y) are both non-singular, and this map is a finite surjective map. In this paper (Part II), we prove that it is a Galois covering. Markman already obtained a similar result in the compact case, which was a motivation of this paper. As an application, we shall construct explicitly the universal Poisson deformation of the normalization \tilde{O} of a nilpotent orbit closure \bar{O} in a complex simple Lie algebra when \tilde{O} has a crepant resolution.
Keywords
Cite
@article{arxiv.0902.2832,
title = {Poisson deformations of affine symplectic varieties II},
author = {Yoshinori Namikawa},
journal= {arXiv preprint arXiv:0902.2832},
year = {2011}
}
Comments
Final version, 31 page, to appear in Nagata memorial issue of Kyoto Journal of Mathematics