Knutson ideals of generic matrices

Abstract

In this paper we show that determinantal ideals of generic matrices are Knutson ideals. This fact leads to a useful result about Gröbner bases of certain sums of determinantal ideals. More specifically, given $I=I_1+\dots +I_k$ a sum of ideals of minors on adjacent columns or rows, we prove that the union of the Gröbner bases of the $I_j$'s is a Gröbner basis of $I$.