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 Gr\"obner bases of certain sums of determinantal ideals. More specifically, given I=I1+…+Ik a sum of ideals of minors on adjacent columns or rows, we prove that the union of the Gr\"obner bases of the Ij's is a Gr\"obner basis of I.
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