INVARIANT HILBERT SCHEMES AND DESINGULARIZATIONS OF QUOTIENTS BY CLASSICAL GROUPS

被引:4
作者
Terpereau, R. [1 ]
机构
[1] Univ Grenoble 1, Inst Fourier, UMR CNRS UJF 5582, F-38402 St Martin Dheres, France
关键词
MCKAY CORRESPONDENCE;
D O I
10.1007/s00031-014-9253-1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let W be a finite-dimensional representation of a reductive algebraic group G. The invariant Hilbert scheme 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 is a smooth variety, and thus for which the Hilbert-Chow morphism is a canonical desingularization of the categorical quotient.
引用
收藏
页码:247 / 281
页数:35
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