Determinacy of determinantal varieties

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 an m × n -matrix. In this note, we consider 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 (Singul Appl 267:119–131, 2009 ). In this note, we prove that matrices parametrized by generic homogeneous forms of degree d define EIDS. It follows that G -finite determinacy of matrices holds in general. As a consequence, EIDS of a given type ( m , n , t ) holds in general.