2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70243Let 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.28 pagesAlgebraic GeometryRepresentation Theory14L30; 16G10text