Poisson deformations of symplectic quotient singularities

  title={Poisson deformations of symplectic quotient singularities},
  author={Victor Ginzburg},
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 ⊂ 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 cohomology H q (X, C) of any smooth… CONTINUE READING
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