2013/01/17 by Ronan Terpereau, Terpereau, Ronan · 2 citations
#Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Algebraic structures and combinatorial models
paper · pdf · doi:10.1007/s00031-014-9253-1
Let W be a finite-dimensional representation of a reductive algebraic group G. The invariant Hilbert scheme H is a moduli space that classifies the G-stable closed subschemes Z of W such that the affine algebra k[Z] is the direct sum of simple G-modules with prescribed multiplicities. In this article, we consider the case where G is a classical group acting on a classical representation W and k[Z] is isomorphic to the regular representation of G as a G-module. We obtain families of examples where H is a smooth variety, and thus for which the Hilbert-Chow morphism γ: H → W//G is a canonical desingularization of the categorical quotient.