On 4-generated bundles and directly linked subcanonical curves
type: Item
instance of: scholarly article
title: On 4-generated bundles and directly linked subcanonical curves
zbMATH Open document ID: 0598.14048
DOI: 10.1016/0021-8693(86)90066-9
author: Luca Chiantini
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: Two curves \(\Gamma\), \(\Gamma\) ' in the complex projective space \({\mathbb{P}}^ 3\) are said to be directly linked if \(\Gamma\) \(\cup \Gamma '\) is the complete intersection of two surfaces. (This makes sense even if the curves are non-reduced or have a common component.) The author considers the case where \(\Gamma\) and \(\Gamma\) ' are both subcanonical in the sense that their canonical classes extend to line bundles on \({\mathbb{P}}^ 3\), or equivalently that they are the 0-loci of sections of rank-2 bundles E and E' on \({\mathbb{P}}^ 3\). He shows that E is then 4- generated in the sense that there is a surjection \(\oplus^{4}{\mathcal O}(- a_ i)\to E.\quad (The\) general bundle is 5-generated.) Moreover, although this surjection is not unique, the numbers \(a_ i\) are determined; it follows, that for a given subcanonical curve \(\Gamma\), there are at most three possibilities for the numerical characters of \(\Gamma\) '.
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 3964047
zbMATH Keywords: linkage
zbMATH Keywords: directly linked curves
zbMATH Keywords: numerical characters of subcanonical curve
zbMATH Keywords: liaison
reviewed by: P. E. Newstead
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90066-9
OpenAlex ID: W2083215498
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description: scientific article; zbMATH DE number 3964047