Projective images of Kummer surfaces
type: Item
instance of: scholarly article
title: Projective images of Kummer surfaces
zbMATH Open document ID: 0793.14029
DOI: 10.1007/BF01459777
author: Thomas Bauer
published in: Mathematische Annalen
publication date: 1994-08-25T00:00:00Z
full work available at URL: https://eudml.org/doc/165203
review text: We consider the linear systems of even resp. odd sections in the powers \({\mathcal L}^ d_ 0\), \(d \geq 2\), of an ample symmetric line bundle \({\mathcal L}_ 0\) on an abelian surface \(A\). These systems define rational maps of the smooth Kummer surface associated to \(A\). We prove that, apart from certain exceptions, these maps are birational morphisms of the smooth Kummer surface onto its image. They contract the \((-2)\)-curves associated to the even resp. odd halfperiods of \({\mathcal L}_ 0\). We classify the exceptional cases, i.e. the cases where (1) the linear system has a base component; or (2) where the morphism is of degree two; or (3) where it contracts additional curves.
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14J60
zbMATH DE Number: 590007
zbMATH Keywords: odd sections
zbMATH Keywords: even sections
zbMATH Keywords: ample symmetric line bundle
zbMATH Keywords: abelian surface
zbMATH Keywords: Kummer surface
reviewed by: Tilman Bauer
MaRDI profile type: Publication
cites work: Symmetric theta-structures
cites work: Q4023939
cites work: On smooth quartic embedding of Kummer surfaces
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cites work: Vector bundles of rank 2 and linear systems on algebraic surfaces
cites work: Projective Models of K - 3 Surfaces
cites work: Bounds on the degree of the equations defining Kummer varieties
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description: scientific article; zbMATH DE number 590007