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 + … + I k I=I_1+\ldots +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 I_j ’s is a Gröbner basis of I I .