Poisson deformations of affine symplectic varieties

Abstract

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 $C^{\ast }$-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.

Version 7(36 pages)

References in corpus (2)

• Induced nilpotent orbits and birational geometry
• Birational geometry and deformations of nilpotent orbits

Cited by in corpus (19)

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