On Castelnuovo-Mumford regularity of products of monomial ideals
type: Item
instance of: scholarly article
title: On Castelnuovo-Mumford regularity of products of monomial ideals
zbMATH Open document ID: 1120.13012
published in: Acta Mathematica Vietnamica
publication date: 2006-01-24T00:00:00Z
review text: In [Collect. Math. 54, No. 2, 137--152 (2003; Zbl 1074.13004)] \textit{A. Conca} and \textit{J. Herzog} asked whether \(\text{reg}(I_1I_2\cdots I_d)\leq \text{reg}(I_1)+\cdots+ \text{reg}(I_d)\) in case each \(I_i\) is generated by a regular sequence. The author proves that this is the case if \(d=2\), \(I_1\) and \(I_2\) are monomial ideals and \(I_1\) is generated by two monomials. The problem can be reduced to the case of square free monomial ideals by passing to the polarization. Then the regularity can be expressed in terms of the reduced homology of the associated simplicial complexes, which is calculated via the Maier-Vietoris sequence.
reviewed by: Emanuela De Negri
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13F55
zbMATH DE Number: 5001050
zbMATH Keywords: Castelnuovo-Mumford regularity
zbMATH Keywords: monomial ideals
zbMATH Keywords: polarization
author: Nguyên Công Minh
describes a project that uses: CoCoA
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5001050