2-spanned surfaces of sectional genus six
type: Item
instance of: scholarly article
title: 2-spanned surfaces of sectional genus six
zbMATH Open document ID: 0814.14007
DOI: 10.1007/BF01765849
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1995-06-20T00:00:00Z
review text: Let \(L\) be a \(k\)-spanned line bundle on a complex projective smooth surface \(S\). This essentially means that the global sections of \(L\) separate suitable 0-cycles of length \(k + 1\) on \(S\). The precise definition and an extensive study can be found in a paper by \textit{M. Beltrametti} and \textit{A. J. Sommese} [cf. Algebraic Geometry, Proc. Int. Conf., L'Aquila 1988, Lect. Notes Math. 1417, 24-51 (1990; Zbl 0706.14007)]; there the pairs \((S,L)\) with \(k > 1\) and \(g(L) < 6\) are classified. -- In the paper under review the cases \(g(L) = 6\) and \(g(L) = 7\), \(k = 3\) are considered. As corollaries the author points out the pairs \((S,L)\) with \(L\) 2-spanned (3-spanned respectively) and degree \(< 11\) and (\(<13\) respectively). The main difficulty to overcome is to make any admissible list effective, i.e. to decide whether for some possible pair \((S,L)\), \(L\) is actually \(k\)-spanned.
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14J10
zbMATH DE Number: 590106
zbMATH Keywords: sectional genus
zbMATH Keywords: del Pezzo surface
zbMATH Keywords: \(k\)-spanned line bundle
author: Antonio Lanteri
reviewed by: Marino Palleschi
MaRDI profile type: Publication
cites work: Q3487533
cites work: A Characterization of the Veronese Surface
cites work: Q3487534
cites work: On Reider's method and higher order embeddings
cites work: Q4195061
cites work: Q3919817
cites work: Q4143433
cites work: Q4748281
cites work: Q4748259
cites work: Classification of algebraic surfaces with sectional genus less than or equal to six. I: Rational surfaces
cites work: On the existence of some surfaces
cites work: Hyperplane sections of projective surfaces. I: The adjunction mapping
cites work: On the adjunction mapping
full work available at URL: https://doi.org/10.1007/bf01765849
OpenAlex ID: W2018076026
description: scientific article; zbMATH DE number 590106