Determinacy of Determinantal Varieties

Abstract

A more general class than complete intersection singularities is the class of determinantal singularities. They are defined by the vanishing of all the minors of a certain size of a $m\times n$-matrix. In this note, we consider $\mathcal{G}$-finite determinacy of matrices defining a special class of determinantal varieties. They are called essentially isolated determinantal singularities (EIDS) and were defined by Ebeling and Gusein-Zade. In this note, we prove that matrices parametrized by generic homogeneous forms of degree $d$ define EIDS. It follows that $\mathcal{G}$-finite determinacy of matrices hold in general. As a consequence, EIDS of a given type $(m,n,t)$ holds in general.

10 pages

References in corpus (2)

• Finite determinacy of matrices over local rings.II. Tangent modules to the miniversal deformations for group-actions involving the ring automorphisms
• Properties of G-Equivalence of Matrices

Cited by in corpus (1)

• Group actions on matrices over local rings. Annihilators of T^1-modules for the groups \mathcal{G}_{lr} , \mathcal{G}_{congr}