Hilbert schemes and noncommutative deformations of type A Kleinian singularities

Let Hk be a symplectic reflection algebra corresponding to a cyclic subgroup of order n and Uk=eHke the spherical subalgebra of Hk. We show that for suitable k there is a filtered -algebra R such that (1) there is an equivalence of categories R-qgr Uk-mod; (2) there is an equivalence of categories . Here is the category of coherent sheaves on the Γ-Hilbert scheme and, for a graded algebra , we write for the quotient category of finitely generated graded -modules modulo torsion.