Gröbner bases of powers of ideals of maximal minors
type: Item
instance of: scholarly article
title: Gröbner bases of powers of ideals of maximal minors
zbMATH Open document ID: 0899.13013
DOI: 10.1016/S0022-4049(96)00061-8
author: Aldo Conca
published in: Journal of Pure and Applied Algebra
publication date: 1998-11-08T00:00:00Z
review text: Let \(K\) be a field and let \(I=I_m\subset K[{\mathbf X}]\) denote the ideal of the polynomial ring \(K[{\mathbf X}]\) generated by the maximal minors of the \(m\times n\) (\(m\leq n\)) generic matrix \(({\mathbf X})\). It is a well known repeatedly proved result that the maximal minors themselves form a Gröbner basis of \(I\) under the so called diagonal order of the monomials of \(K[{\mathbf X}]\). The present paper extends this result to the powers of \(I\), namely, a Gröbner basis of the power \(I^r\) is constituted by the \(r\)-products of maximal minors. The main tool is the Knuth-Robinson-Schensted correspondence. A formula for the Hilbert series of the residue rings \(K[{\mathbf X}]/I^r\) is also given.
Mathematics Subject Classification ID: 13C40
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 1089291
zbMATH Keywords: Gröbner basis
zbMATH Keywords: monomials
zbMATH Keywords: Hilbert series
zbMATH Keywords: determinantal ideals
reviewed by: Aron Simis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1089291