Complex surfaces polarized by an ample and spanned line bundle of genus three
type: Item
instance of: scholarly article
title: Complex surfaces polarized by an ample and spanned line bundle of genus three
zbMATH Open document ID: 0707.14033
DOI: 10.1007/BF00147460
author: Elvira Laura Livorni
author: Antonio Lanteri
published in: Geometriae Dedicata
publication date: 1989-01-01T00:00:00Z
review text: Let X be a nonsingular projective surface and L an ample line bundle on X. Its sectional genus \(g\) is defined by the formula \(2g-2=L\cdot (K\otimes L)\), where K is the canonical bundle on X. It is further assumed that L is spanned by its global sections. In the paper under review the authors classify all such pairs (X,L) with \(g=3\) (The cases \(g\leq 2\) are known previously). These are: (1) a double plane, (2) elliptic surfaces with multiple fibres and (3) ruled surfaces, and the third case is further classified. As remarked at the end of the paper, the same classification was independently carried out by \textit{H. Maeda} [Sci. Pap. Coll. Arts. Sci., Univ. Tokyo 37, No.2, 103-112 (1988)] without assuming that L is spanned by its global sections.
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 4160934
zbMATH Keywords: spanned by global sections
zbMATH Keywords: polarized surfaces
zbMATH Keywords: adjunction process
zbMATH Keywords: ample line bundle
zbMATH Keywords: sectional genus
reviewed by: Eiji Horikawa
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4160934