A constructive method for standard Borel fixed submodules with given extremal Betti numbers
type: Item
instance of: scholarly article
title: A constructive method for standard Borel fixed submodules with given extremal Betti numbers
zbMATH Open document ID: 1397.13002
author: Marilena Crupi
published in: Mathematics
publication date: 2018-07-05T00:00:00Z
review text: Summary: Let \(S\) be a polynomial ring in \(n\) variables over a field \(K\) of any characteristic. Given a strongly stable submodule \(M\) of a finitely generated graded free \(S\)-module \(F\), we propose a method for constructing a standard Borel-fixed submodule \(\widetilde{M}\) of \(F\) so that the extremal Betti numbers of \(M\), values as well as positions, are preserved by passing from \(M\) to \(\widetilde{M}\). As a result, we obtain a numerical characterization of all possible extremal Betti numbers of any standard Borel-fixed submodule of a finitely generated graded free \(S\)-module \(F\).
Mathematics Subject Classification ID: 13A02
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 13D40
zbMATH DE Number: 6898685
zbMATH Keywords: graded modules
zbMATH Keywords: monomial modules
zbMATH Keywords: minimal graded resolution
zbMATH Keywords: extremal Betti numbers
describes a project that uses: Macaulay2
describes a project that uses: CoCoALib
MaRDI profile type: Publication
full work available at URL: math5040056
OpenAlex ID: W2765131806
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DOI: 10.3390/MATH5040056
description: scientific article; zbMATH DE number 6898685