Poisson deformations of affine symplectic varieties II

Let Y be an affine symplectic variety of dimension 2n, and let π : X → Y be a crepant resolution. By the definition, there is a symplectic 2-form σ̄ on the smooth part Yreg ∼= π (Yreg), and it extends to a 2-form σ on X. Since π is crepant, σ is a symplectic 2-form on X. The symplectic structures on X and Y define Poisson structures on them in a natural manner. One can define a Poisson deformation of X (resp. Y ) (cf. [Na 1]). For X, a Poisson deformation is equivalent to a symplectic deformation, namely a deformation of the pair (X, σ). Assume that Y has a C-action with positive weight, and with a unique fixed point 0 ∈ Y . Then this C-action extends to a C-action on X. By [Na 2] one can construct a C-equivariant commutative diagram