Curves and \(0\)-cycles on projective surfaces
type: Item
instance of: scholarly article
title: Curves and \(0\)-cycles on projective surfaces
zbMATH Open document ID: 0827.14005
DOI: 10.1007/BF01264099
author: Marco Andreatta
author: E. Ballico
published in: Geometriae Dedicata
publication date: 1995-12-11T00:00:00Z
review text: Let \(S\) be a smooth projective surface containing a smooth curve \(C\) endowed with a linear series of dimension 1 and degree \(n\). The points of any divisor in that series are easily seen to be mapped by the rational map \(f\) defined by \(|K_S + C |\) to linearly dependent points, thus spanning a linear space of dimension \(n' < n - 1\). The case \(n'\) small (especially \(n' = 1)\) is studied via the adjunction map \(f\) using the Bogomolov-Reider techniques. On top of other results, the authors show that the property \(n' = 1\) essentially leads to the surfaces whose hyperplane sections are either trigonal or hyperlliptic curves, if \(C\) is very ample.
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14C17
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 14J25
zbMATH DE Number: 663732
zbMATH Keywords: hyperplane sections of surfaces
zbMATH Keywords: linear series
zbMATH Keywords: adjunction map
reviewed by: Marino Palleschi
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01264099
OpenAlex ID: W1970295398
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description: scientific article; zbMATH DE number 663732