On the number of equations defining certain varieties
type: Item
instance of: scholarly article
title: On the number of equations defining certain varieties
zbMATH Open document ID: 0874.14044
DOI: 10.1007/BF02567968
author: Margherita Barile
published in: Manuscripta Mathematica
publication date: 1997-04-13T00:00:00Z
full work available at URL: https://eudml.org/doc/156243
review text: The author considers the minimal number of equations needed to define the variety \(V(I)\) associated to a monomial ideal \(I\) of a polynomial ring, this number is called the arithmetical rank and denoted by \(\text{ara}(I)\). The author generalizes a lemma of \textit{Th. Schmitt} and \textit{W. Vogel} [Math. Ann. 245, 247-253 (1979; Zbl 0408.14014)]; given conditions on a decomposition of a system of generators of \(I\), she can construct a system \(J\) of elements in \(I\) with cardinal less than the minimal number of generators of \(I\) and such that \(\text{rad}(J)= \text{rad}(I)\), where \((J)\) is the ideal generated by \(J\). This criterium has several interesting applications to a class of ideals, where the author computes \(\text{ara}(I)\).
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 14M10
zbMATH DE Number: 980725
zbMATH Keywords: minimal number of equations
zbMATH Keywords: monomial ideal
zbMATH Keywords: arithmetical rank
reviewed by: Marcel Morales
MaRDI profile type: Publication
cites work: Cohomological dimension of algebraic varieties
cites work: Q3699817
cites work: A new explicit finite free resolution of ideals generated by monomials in an R-sequence
cites work: On set-theoretic intersections and connectedness of algebraic varieties in \(\mathbb P^n\)
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description: scientific article; zbMATH DE number 980725