Castelnuovo-Mumford regularity of products of ideals

2002/10/04 by Aldo Conca, Conca, Aldo, Juergen Herzog +1 · 13 citations
Computer Science · Mathematics · #13D02 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC #msc:13D02

paper · pdf · doi:10.48550/arxiv.math/0210065

14 pages

arxiv created 2002/10/04 · openalex publication_date 2002/10/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the behavior of the Castelnuovo-Mumford regularity under certain operations on ideals and modules, like products or powers. In particular, we show that reg(IM) can be larger than reg(M)+reg(I) even when I is an ideal of linear forms and M is a module with a linear resolution. On the other hand, we show that any product of ideals of linear forms has a linear resolution. We also discuss the case of polymatroidal ideals and show that any product of determinantal ideals of a generic Hankel matrix has a linear resolution.

Cited by

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• k-shellable simplicial complexes and graphs
• The saturation number of powers of graded ideals
• A note on the regularity of products
• Integrally closed and componentwise linear ideals
• Geometric regularity of powers of two-dimensional squarefree monomial ideals
• Pretty clean monomial ideals and linear quotients
• Monomial ideals with linear quotients and componentwise (support-)linearity
• Hilbert series of subspace arrangements
• Linearization of monomial ideals
• Monomial ideals whose powers have a linear resolution
• Symbolic powers of edge ideals of graphs
• Bounds on the Castelnuovo-Mumford regularity of tensor products

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• Asymptotic linear bounds for the Castelnuovo-Mumford regularity