Abstract
We prove that the Poisson deformation functor of an affine (singular) symplectic variety is unobstructed. As a corollary, we prove the following result. For an affine symplectic variety with a good -action (where its natural Poisson structure is positively weighted), the following are equivalent.
(1) has a crepant projective resolution.
(2) has a smoothing by a Poisson deformation.
A typical example is (the normalization) of a nilpotent orbit closure in a complex simple Lie algebra. By the theorem, one can see which orbit closure has a smoothing by a Poisson deformation.
Citation
Yoshinori Namikawa. "Poisson deformations of affine symplectic varieties." Duke Math. J. 156 (1) 51 - 85, 15 January 2011. https://doi.org/10.1215/00127094-2010-066
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