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 πinduces 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.

Final version, 31 page, to appear in Nagata memorial issue of Kyoto Journal of Mathematics

References in corpus (4)

• Poisson deformations of affine symplectic varieties
• Induced nilpotent orbits and birational geometry
• Birational geometry and deformations of nilpotent orbits
• On deformations of Q-factorial symplectic varieties

Cited by in corpus (21)

• Yangians and quantizations of slices in the affine Grassmannian
• Prime exceptional divisors on holomorphic symplectic varieties and monodromy-reflections
• Slodowy Slices and Universal Poisson Deformations
• Counting resolutions of symplectic quotient singularities
• On 81 symplectic resolutions of a 4-dimensional quotient by a group of order 32
• Short Star-Products for Filtered Quantizations, I
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• The universal Poisson deformation of hypertoric varieties and some classification results
• On the structure of homogeneous symplectic varieties of complete intersection
• Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal{N}=4$ non-Abelian quiver gauge theories
• On modular categories O for quantized symplectic resolutions
• Affine Springer Fibers, Procesi bundles, and Cherednik algebras
• Birational geometry for the covering of a nilpotent orbit closure II
• Birational geometry for nilpotent orbits
• Springer theory for symplectic Galois groups
• The diagonal coinvariant ring of a complex reflection group
• Automorphism groups of deformations and quantizations of Kleinian singularities
• Partial Resolutions of Affine Symplectic Singularities
• Crepant resolutions of stratified varieties via gluing
• Namikawa-Weyl groups of affinizations of smooth Nakajima quiver varieties
• Localization theorems for quantized symplectic resolutions