On the graded resolution of ideals of a few general fat points of \(\mathbb P^n\)
type: Item
instance of: scholarly article
title: On the graded resolution of ideals of a few general fat points of \(\mathbb P^n\)
zbMATH Open document ID: 1066.13012
published in: Journal of Pure and Applied Algebra
publication date: 2005-06-01T00:00:00Z
review text: Let \(I\) be the ideal of \(r+1<n+1\) general fat points of \(\mathbb P^n\) with multiplicities \((a,b,\ldots,b),\) where \(a\geq 2b.\) The graded Betti numbers of \(I\) are explicitly computed. The hypotheses permit to say that \(I\) is projectively equivalent to a monomial splittable ideal [the notion of splittable ideal was introduced by \textit{S. Eliahou} and \textit{M. Kervaire}, J. Algebra 129, 1--25 (1990; Zbl 0701.13006)]. So a sequence of splittings of \(I\) is performed, using ideals whose graded Betti numbers can easily be computed. Finally the graded Betti numbers of \(I\) are recovered from those of such ideals.
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 14M05
zbMATH DE Number: 2173216
zbMATH Keywords: fat points
zbMATH Keywords: graded Betti numbers
zbMATH Keywords: monomial splittable ideal
author: Giuliana Fatabbi
author: Anna Lorenzini
reviewed by: Giuseppe Zappalà
describes a project that uses: CoCoA
MaRDI profile type: Publication
full work available at URL: j.jpaa.2004.10.010
OpenAlex ID: W2154527494
cites work: Minimal resolutions of some monomial ideals
cites work: On the resolution of ideals of fat points
cites work: Q5589310
cites work: Betti numbers of some monomial ideals
DOI: 10.1016/J.JPAA.2004.10.010
description: scientific article; zbMATH DE number 2173216