Trigonal hyperplane sections of projective surfaces
type: Item
instance of: scholarly article
title: Trigonal hyperplane sections of projective surfaces
zbMATH Open document ID: 0729.14028
DOI: 10.1007/BF02568748
author: Maria Lucia Fania
published in: Manuscripta Mathematica
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155511
review text: Let X be a smooth surface in \({\mathbb{P}}^ n\). Assume that at least one of the hyperplane sections, C, of X is a smooth r-gonal curve. Then it is a quite classical question to describe the pair (X,L) with \(L\cong {\mathcal O}_ X(C)\). - If \(r=2\) there is a complete description of surfaces containing at least one hyperelliptic hyperplane section. This is due to Serrano, Sommese and Sommese-Van de Ven. If \(r>2\) there are only partial results due to Serrano. In the paper the case \(r=3\) is completely worked out. The main tools are adjunction theory results and Reider's type results.
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 14C17
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 4204548
zbMATH Keywords: 3-gonal curves
zbMATH Keywords: adjoint line bundle
zbMATH Keywords: hyperplane sections
zbMATH Keywords: adjunction
reviewed by: Mauro C. Beltrametti
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4204548