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Regularity in codimension one of orbit closures in module varieties

Grzegorz Zwara
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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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Grzegorz Zwara. 2004-11-14. Regularity in codimension one of orbit closures in module varieties. https://arxiv.org/abs/math/0402359

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