The regularity index of up to \(2n-1\) equimultiple fat points of \(\mathbb{P}^n\)
type: Item
instance of: scholarly article
title: The regularity index of up to \(2n-1\) equimultiple fat points of \(\mathbb{P}^n\)
zbMATH Open document ID: 1354.13021
author: Giuliana Fatabbi
author: Anna Lorenzini
author: Gabriele Calussi
published in: Journal of Pure and Applied Algebra
publication date: 2017-01-23T00:00:00Z
review text: For any \(P\in \mathbb {P}^n\) and any integer \(m>0\) let \(mP\) be the closed subscheme of \(\mathbb {P}^n\) with \((\mathcal {I}_P)^m\) as its ideal sheaf. A fat scheme \(X\subset \mathbb {P}^n\) is a finite disjoint union of schemes \(m_iP_i\). Trung and, independently, Fatabbi and Lorenzini, conjectured a sharp upper bound for the regularity index of a fat scheme (it is called Segre's bound). In this paper the authors give an affermative answer to the equimultiple case (all \(m_i\) are the same) for a low number of points. Later, Segre's conjecture was solved by \textit{U. Nagel} and \textit{B. Trok} [``Segre's regularity bound for fat points schemes'', Preprint, \url{arXiv:1611.06279}].
Mathematics Subject Classification ID: 13D40
Mathematics Subject Classification ID: 14C20
zbMATH DE Number: 6676884
zbMATH Keywords: fat point scheme
zbMATH Keywords: regularity index
zbMATH Keywords: Segre conjecture
zbMATH Keywords: Castelnuovo-Mumford regularity
zbMATH Keywords: Hilbert function
reviewed by: E. Ballico
describes a project that uses: CoCoA
MaRDI profile type: Publication
full work available at URL: j.jpaa.2016.10.002
OpenAlex ID: W2547515447
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cites work: On Segre bound for the regularity index of fat points in \(\mathbb{P}^2\)
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cites work: On the regularity index of \(n+3\) almost equimultiple fat points in \(\mathbb P^n\)
DOI: 10.1016/J.JPAA.2016.10.002
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description: scientific article; zbMATH DE number 6676884