Quantization of minimal resolutions of Kleinian singularities

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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 n-th 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^λof 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^λas quantum Hamiltonian reductions, due to Holland, and a GIT construction of minimal resolutions of X, due to Cassens and Slodowy.
LaTeX, 24 pages. Version 2 (some misprints fixed)

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Representation Theory, Algebraic Geometry, Quantum Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/98955

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0505165
 http://arxiv.org/abs/math/0505165

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arXiv