RATIONAL SINGULARITIES OF G-SATURATION

被引：1

作者：

Ngo, Nham, V ^{[1
]}

机构：

[1] Univ North Georgia, Dept Math, Oakwood, GA 30566 USA

来源：

JOURNAL OF COMMUTATIVE ALGEBRA | 2018年 / 10卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Rational resolution (singularities); algebraic groups; G-saturation varieties; commuting varieties; homogeneous bundles; cohomology; NILPOTENT COMMUTING VARIETIES; FLAG VARIETIES; LIE-ALGEBRAS; BUNDLES; COHOMOLOGY; THEOREM;

D O I：

10.1216/JCA-2018-10-3-375

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a semisimple algebraic group defined over an algebraically closed field of characteristic 0 and P a parabolic subgroup of G. Let M be a P-module and V a P-stable closed subvariety of M. We show in this paper that, if the varieties V and G . M have rational singularities, and the induction functor R-i ind(P)(G)(-) satisfies certain vanishing conditions, then the variety G . V has rational singularities. This generalizes a result of Kempf [8] on the collapsing of homogeneous bundles. As an application, we prove the property of having rational singularities for nilpotent commuting varieties over 3 x 3 matrices.

引用

页码：375 / 391

页数：17

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[2]

BRUNS W, 1988, LECT NOTES MATH, V1327, P1

[3] VERY SIMPLE PROOF OF BOTTS THEOREM [J].