Regularity in codimension one of orbit closures in module varieties
Abstract
Let M_d(k) denote the space of dxdmatrices 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2004
 arXiv:
 arXiv:math/0402359
 Bibcode:
 2004math......2359Z
 Keywords:

 Algebraic Geometry;
 Representation Theory;
 14L30;
 16G10
 EPrint:
 28 pages