Knutson ideals of generic matrices

2021/01/16 by Lisa Seccia, Seccia, Lisa
Mathematics · #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2101.06496

openalex publication_date 2021/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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=I₁+…+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.

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