Generic projections, the equations defining projective varieties and Castelnuovo regularity
type: Item
instance of: scholarly article
title: Generic projections, the equations defining projective varieties and Castelnuovo regularity
zbMATH Open document ID: 0971.14001
DOI: 10.1007/PL00004809
author: Sijong Kwak
published in: Mathematische Zeitschrift
publication date: 2000-12-04T00:00:00Z
review text: Let \(X\subset\mathbb{P}^N\) be a reduced, irreducible projective variety of degree \(d\) and codimension \(e\geq 4\) and let \(\text{reg}(X)\) be the Castelnuovo-Mumford regularity of \(X\). If \(X\) is smooth of dimension 5 (resp. 6) it is shown that \(\text{reg}(X) \leq(d-e+1) +10\) (resp. \((d-e+1)+20)\). Moreover, for reduced, connected equidimensional locally Cohen-Macaulay curves or surfaces, upper bounds for \(\text{reg}(X)\) are given in terms of \(d,e\) and the arithmetic genus.
reviewed by: Cristodor-Paul Ionescu
Mathematics Subject Classification ID: 14A05
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 14J99
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 1502083
zbMATH Keywords: Castelnuovo-Mumford regularity
zbMATH Keywords: Cohen-Macaulay curves
zbMATH Keywords: arithmetic genus
zbMATH Keywords: Cohen-Macaulay surfaces
MaRDI profile type: Publication
full work available at URL: pl00004809
OpenAlex ID: W2091249048
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description: scientific article; zbMATH DE number 1502083