On the multiplicity of multigraded modules over Artinian local rings
type: Item
instance of: scholarly article
title: On the multiplicity of multigraded modules over Artinian local rings
zbMATH Open document ID: 1217.13010
author: Nguyen Tien Manh
author: Duong Quoc Viet
published in: Tokyo Journal of Mathematics
publication date: 2011-03-25T00:00:00Z
review text: Let \(S\) be a finitely generated standard multigraded algebra over an Artinian local ring \(A\) and let \(M\) be a finitely generated multigraded \(S\)-module. The paper under review first investigates the relationship between the multiplicity and mixed multiplicities of \(M\). More precisely, the main result of Section 2 of the paper expresses the multiplicity of \(M\) as a sum of its mixed multiplicities. In that way the authors achieve a ``perfect version'' of Theorem 4.3 from [\textit{M. Herrmann, E. Hyry, J. Ribbe} and \textit{Z. Tang}, J.~Algebra 197, No. 2, 311--341 (1997; Zbl 0931.13002)]. Then in Section 3 the authors give some applications of Section 2 to multigraded fiber cones.
reviewed by: Hamid Kulosman
Mathematics Subject Classification ID: 13H15
Mathematics Subject Classification ID: 13A02
Mathematics Subject Classification ID: 13E10
zbMATH DE Number: 5869968
zbMATH Keywords: Artinian rings
zbMATH Keywords: mixed multiplicities
zbMATH Keywords: multigraded modules
zbMATH Keywords: Hilbert-Samuel polynomials
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1296483474
OpenAlex ID: W2087164159
cites work: Q3247189
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DOI: 10.3836/TJM/1296483474
description: scientific article; zbMATH DE number 5869968