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INVARIANT HILBERT SCHEMES AND DESINGULARIZATIONS OF QUOTIENTS BY CLASSICAL GROUPS

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Let W be a finite-dimensional representation of a reductive algebraic group G. The invariant Hilbert scheme \( \mathcal{H} \) 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 \( \mathcal{H} \) is a smooth variety, and thus for which the Hilbert–Chow morphism \( \gamma :\mathcal{H}\to W//G \) is a canonical desingularization of the categorical quotient.

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  1. Université Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF BP 74, 38402, St. Martin d’Hères Cédex, France

    R. TERPEREAU

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TERPEREAU, R. INVARIANT HILBERT SCHEMES AND DESINGULARIZATIONS OF QUOTIENTS BY CLASSICAL GROUPS. Transformation Groups 19, 247–281 (2014). https://doi.org/10.1007/s00031-014-9253-1

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  • DOI: https://doi.org/10.1007/s00031-014-9253-1

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