A finite classification of \((x, y)\)-primary ideals of low multiplicity
type: Item
instance of: scholarly article
title: A finite classification of \((x, y)\)-primary ideals of low multiplicity
zbMATH Open document ID: 1392.13003
author: Paolo Mantero
author: Jason McCullough
published in: Collectanea Mathematica
publication date: 2018-02-20T00:00:00Z
review text: If \(p=(x,y)\) is an ideal generated by two independent linear forms in a polynomial ring \(S\) over an algebraically closed field \(k\), one gives a (finite, i.e. one gives low degree generators) classification of \(p\)-primary ideals of multiplicity \(e(S/I)=3\) or \(e(S/I)=4\). In other contexts, similar classifications for the local case (i.e. rings of formal powers) or multiple structures on lines (or linear spaces) can be found in the papers quoted in the references or in the references of the quoted papers. In the case considered here the lists are particularly long. The authors give a good motivation for the interest of the subject.
reviewed by: Nicolae Manolache
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 13D02
zbMATH DE Number: 6841311
zbMATH Keywords: primary ideal
zbMATH Keywords: projective dimension
zbMATH Keywords: multiple structures
describes a project that uses: Macaulay2
MaRDI profile type: Publication
full work available at URL: s13348-017-0196-4
OpenAlex ID: W2604172141
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DOI: 10.1007/S13348-017-0196-4
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description: scientific article; zbMATH DE number 6841311