Numerical Burniat and irregular surfaces
type: Item
instance of: scholarly article
title: Numerical Burniat and irregular surfaces
zbMATH Open document ID: 1062.14049
DOI: 10.1023/A:1022392129474
author: Ezio Stagnaro
published in: Acta Applicandae Mathematicae
publication date: 2003-04-27T00:00:00Z
review text: The author constructs new examples of surfaces of general type as double planes, that is as double covers of \(\mathbb{P}^2\). More precisely he constructs: a surface with \(p_g=q=0\), \(P_2=4\) as double plane with branch locus of degree \(12\) having five irreducible components; a surface with \(p_g=q=1\), \(P_2=4\) as double plane with branch locus of degree \(12\) having four irreducible components; a surface with \(p_g=q=0\), \(P_2=5\) as double plane with branch locus of degree \(14\) having six irreducible components; a surface with \(p_g=q=0\), \(P_2=4\) as double plane with irreducible branch locus of degree \(22\). The first three examples have a bicanonical map that is not birational, and a torsion group different from zero (more precisely there are non trivial 2-torsion elements in the Picard group arising from irreducible components of the branch locus). All constructions are explicit: the author gives the equations of the branch curves. The results are presented without complete proofs, which will be published elsewhere.
reviewed by: Roberto Pignatelli
Mathematics Subject Classification ID: 14J29
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 14E20
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 1901298
zbMATH Keywords: surfaces of general type
zbMATH Keywords: double planes
zbMATH Keywords: branch locus
zbMATH Keywords: bicanonical transformation
MaRDI profile type: Publication
full work available at URL: a:1022392129474
OpenAlex ID: W142712104
description: scientific article; zbMATH DE number 1901298