Poisson deformations of affine symplectic varieties, II

By Y. Namikawa. 2009

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This article is a continuationof previouswork,whichhas the same title. LetY be anaffine symplectic varietywith aC∗-actionwithpositiveweights, and letπ : 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 Part I, we proved that PDef(X) and PDef(Y ) are both nonsingular, and this map is a finite surjective map. In this article (Part II), we prove that it is a Galois covering. Markman already obtained a similar result in the compact case, which was a motivation for this article. As an application, we construct explicitly the universal Poisson deformation of the normalization Õ of a nilpotent orbit closure Ō in a complex simple Lie algebra when Õ has a crepant resolution.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bf7933d84dcabe6bc967ab6daf11745bc1e09a33