Mathematics – Algebraic Geometry
Scientific paper
2009-02-17
Kyoto J. Math. vol 50 (2010) no.4 727-752
Mathematics
Algebraic Geometry
Final version, 31 page, to appear in Nagata memorial issue of Kyoto Journal of Mathematics
Scientific paper
10.1215/0023608X-2010-012
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.
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