Classifications of Determinantal Varieties

Abstract

Let Mns be a space of matrices of order n×s with complex enteries. The determinantal singularities are defined by vanishing of all the minors of a certain size of an n ×s matrix α : Ck → Mns. The class of determinantal singularities is a more general class than the class of complete intersection singularities. The G-finite deteminacy gives a special class of determinantal varieties known as essentially isolated determinantal singularities (EIDS), firstly introduced by Ebeling and Gusein-Zade in 2009. We give a computational method to find linear forms of EIDS by programming in C