  We establish a connection between smooth symplectic resolutions and
symplectic deformations of a (possibly singular) affine Poisson variety.
  In particular, let V be a finite-dimensional complex symplectic vector space
and G\subset Sp(V) a finite subgroup. Our main result says that the so-called
Calogero-Moser deformation of the orbifold V/G is, in an appropriate sense, a
versal Poisson deformation. That enables us to determine the algebra structure
on the rational cohomology H^*(X) of any smooth symplectic resolution X \to V/G
(multiplicative McKay correspondence). We prove further that if G is an
irreducible Weyl group in GL(h) and V=h+ h^* then no smooth symplectic
resolution of V/G exists unless G is of types A,B, or C.

Algebraic Geometry;Differential Geometry;Quantum Algebra;Symplectic Geometry