Regularity in codimension one of orbit closures in module varieties

2004/02/23 by Grzegorz Zwara, Zwara, Grzegorz
Mathematics · #14L30 #16G10 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14L30 #msc:16G10

paper · pdf · doi:10.48550/arxiv.math/0402359

28 pages

openalex publication_date 2004/02/23 · arxiv created 2004/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M_d(k) denote the space of dxd-matrices with coefficients in an algebraically closed field k. Let X be an orbit closure in the product [M_d(k)]^t equipped with the action of the general linear group GL_d(k) by simultaneous conjugation. We show that X is regular at any its point y such that the orbit of y has codimension one in X. The proof uses mainly the representation theory of associative algebras.

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