Castelnuovo-Mumford regularity of simplicial toric rings.
type: Item
instance of: scholarly article
title: Castelnuovo-Mumford regularity of simplicial toric rings.
zbMATH Open document ID: 1080.13504
DOI: 10.1016/S0021-8693(02)00541-0
author: Le Tuan Hoa
author: J. Stückrad
published in: Journal of Algebra
publication date: 2003-04-02T00:00:00Z
review text: Eisenbud and Goto conjectured that the Castelnuovo-Mumford regularity \(\text{reg}(R)\) of a standard graded domain over an algebraically closed field is bounded by the difference \(\text{deg}(R) -\text{codim}(R)\). So far the conjecture has been proved only in a few low-dimensional cases. The authors provide a bound for \(\text{reg}(R)\) in the case where \(R\) is the toric ring defined by a simplicial affine semigroup, namely \[ \text{reg}(R)\leq\min ( \text{codim}(R)(\deg(R)-1),\dim(R)(\text{deg}(R)-\text{codim}(R)-2)+2 ) \] provided \(\deg(R)\geq \text{codim}(R)+2\). Though the bound is certainly weaker than the conjectured one, it can be considered a very good bound since it is linear in \(\text{deg}(R)\). In its proof the authors use various approaches to control the reduction number and the local cohomology of \(R\).
reviewed by: Winfried Bruns
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 14M25
zbMATH DE Number: 1891315
zbMATH Keywords: Castelnuovo-Mumford regularity
zbMATH Keywords: reduction number
zbMATH Keywords: Eisenbud-Gotos conjecture
zbMATH Keywords: standard graded domain
zbMATH Keywords: toric ring
zbMATH Keywords: local cohomology
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1891315