Poisson deformations of affine symplectic varieties

Details Poisson deformations of affine symplectic varieties Poisson deformations of affine symplectic varieties

2006-09-27

arxiv.org/abs/math/0609741v7

Duke Math. J. 156 (2011) 51-85

Mathematics

Algebraic Geometry

Version 7(36 pages)

Scientific paper

10.1215/00127094-2010-066

We shall prove that the Poisson deformation functor of an affine (singular) symplectic variety is unobstructed. As a corollary, we prove the following result. Theorem: For an affine symplectic variety $X$ with a good $C^*$-action (where its natural Poisson structure is positively weighted), the following are equivalent (1) $X$ has a crepant projective resolution. (2) $X$ has a smoothing by a Poisson deformation.

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