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 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. 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.
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