Abstract
In this paper we prove an analogue of a recent result of Gordon and Stafford that relates the representation theory of certain noncommutative deformations of the coordinate ring of the nth symmetric power of C 2 with the geometry of the Hilbert scheme of n points in C 2 through the formalism of Z -algebras. Our work produces, for every regular noncommutative deformation O λ of a Kleinian singularity X = C 2 / Γ , as defined by Crawley-Boevey and Holland, a filtered Z -algebra which is Morita equivalent to O λ , such that the associated graded Z -algebra is Morita equivalent to the minimal resolution of X. The construction uses the description of the algebras O λ as quantum Hamiltonian reductions, due to Holland, and a GIT construction of minimal resolutions of X, due to Cassens and Slodowy.
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