Duke Mathematical Journal
- Duke Math. J.
- Volume 156, Number 1 (2011), 51-85.
Poisson deformations of affine symplectic varieties
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.
Duke Math. J., Volume 156, Number 1 (2011), 51-85.
First available in Project Euclid: 16 December 2010
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Namikawa, Yoshinori. Poisson deformations of affine symplectic varieties. Duke Math. J. 156 (2011), no. 1, 51--85. doi:10.1215/00127094-2010-066. https://projecteuclid.org/euclid.dmj/1292509118