On quasi-polarized surfaces of general type whose sectional genus is equal to the irregularity
type: Item
instance of: scholarly article
title: On quasi-polarized surfaces of general type whose sectional genus is equal to the irregularity
zbMATH Open document ID: 1049.14033
DOI: 10.1023/A:1005016526062
author: Yoshiaki Fukuma
published in: Geometriae Dedicata
publication date: 1999-01-01T00:00:00Z
review text: In the paper under review, the author continues his study of quasi-polarized surfaces \((X,L)\) over the complex number field, whose irregularity \(q(X)\) equals the sectional genus \(g(L)\). He begun this study in the papers [Can. J. Math. 50, No. 6, 1209--1235 (1998; Zbl 0930.14002) and Trans. Am. Math. Soc. 348, No. 10, 4185--4197 (1996; Zbl 0878.14005)], where he classified quasi-polarized surfaces with \(g(L)=q(X)\), such that either the Kodaira dimension is \(\leq 1\), or the Kodaira dimension is \(2\), \(L\) is ample and \(h^0(L)>0\). Here he assumes that the Kodaira dimension is \(2\) and \(h^0(L)>0\), but the hypothesis of ampleness of \(L\) is removed: \(L\) is only assumed to be nef and big. The main theorem asserts that, in this situation, \(h^0(L)=1\) and that, called \(D\) the effective divisor in \(| L|\), \(D\) is reduced and is of one of the following two types: a smooth irreducible curve with \(D^2\leq 4\), or a union of irreducible smooth curves \(C_i\), forming a configuration which is completely described. Several examples are given of the possible situations.
reviewed by: Emilia Mezzetti
Mathematics Subject Classification ID: 14J29
Mathematics Subject Classification ID: 14C20
zbMATH DE Number: 1270421
zbMATH Keywords: quasi-polarized surface
zbMATH Keywords: sectional genus
zbMATH Keywords: irregularity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1270421