Free complexes defining maximal quasi-Buchsbaum graded modules over polynomial rings
type: Item
instance of: scholarly article
title: Free complexes defining maximal quasi-Buchsbaum graded modules over polynomial rings
zbMATH Open document ID: 0794.13009
author: Mutsumi Amasaki
published in: Journal of Mathematics of Kyoto University
publication date: 1994-08-31T00:00:00Z
review text: The author investigates the structure of graded maximal quasi-Buchsbaum modules (MQB-modules, for short) over Gorenstein graded rings. The main results are the theorems (4.5) and (4.10) in section 4. Theorem (4.5) provides a sufficient condition for decomposability of an MQB-module of limite projective dimension; this condition states that (for each \(i)\) the set of all degrees in which the \(i\)-th graded local cohomology of the module does not vanish should be `decomposable' (in a certain sense). Under the extra assumption that at most two local cohomology modules do not vanish and each of them is concentrated in only one degree, there are even more explicit structure results for the given MQB-module (theorem (1.10)). The author's method to prove results about the given module \(M\) is to associate a certain minimal complex of finitely generated free modules to \(M\) and to investigate the structure of those complexes (in sections 2 and 3). At appropriate places the author explains connections and overlappings with recent papers of Yoshino and Cipu, Herzog, Popescu (preprints).
Mathematics Subject Classification ID: 13D25
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 13C13
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 408741
zbMATH Keywords: free complexes
zbMATH Keywords: decomposability
zbMATH Keywords: structure of graded maximal quasi- Buchsbaum modules
zbMATH Keywords: Gorenstein graded rings
zbMATH Keywords: MQB-module
reviewed by: Jürgen Ribbe
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519342
OpenAlex ID: W1603788338
DOI: 10.1215/KJM/1250519342
description: scientific article; zbMATH DE number 408741