Knutson ideals of generic matrices

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 \(I=I_1+\ldots+I_k\) a sum of ideals of minors on adjacent columns or rows, we prove...

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Bibliographic Details
Published in:arXiv.org 2021-01
Main Author: Seccia, Lisa
Format: Article
Language:English
Online Access:Get full text
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Summary: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 \(I=I_1+\ldots+I_k\) a sum of ideals of minors on adjacent columns or rows, we prove that the union of the Gr\"obner bases of the \(I_j\)'s is a Gr\"obner basis of \(I\).
ISSN:2331-8422