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 π: X -> Y be its crepant resolution. Then π 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 O of a nilpotent orbit closure O in a complex simple Lie algebra when O has a crepant resolution.