Poisson deformations of affine symplectic varieties
  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. 
Yoshinori Namikawa