Regularity in codimension one of orbit closures in module varieties

Details Regularity in codimension one of orbit closures in module varieties Regularity in codimension one of orbit closures in module varieties

2004-02-23

arxiv.org/abs/math/0402359v2

Mathematics

Algebraic Geometry

28 pages

Scientific paper

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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