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On Cox rings of K3 surfaces

Part of: Surfaces and higher-dimensional varieties Cycles and subschemes

Published online by Cambridge University Press:  25 March 2010

Michela Artebani ,
Jürgen Hausen  and
Antonio Laface
Michela Artebani
Affiliation:
Departamento de Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile (email: martebani@udec.cl)
Jürgen Hausen
Affiliation:
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany (email: juergen.hausen@uni-tuebingen.de)
Antonio Laface
Affiliation:
Departamento de Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile (email: alaface@udec.cl)
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Abstract

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We study Cox rings of K3 surfaces. A first result is that a K3 surface has a finitely generated Cox ring if and only if its effective cone is rational polyhedral. Moreover, we investigate degrees of generators and relations for Cox rings of K3 surfaces of Picard number two, and explicitly compute the Cox rings of generic K3 surfaces with a non-symplectic involution that have Picard number 2 to 5 or occur as double covers of del Pezzo surfaces.

Keywords

Cox ringsK3 surfaces

MSC classification

Secondary: 14J28: $K3$ surfaces and Enriques surfaces 14C20: Divisors, linear systems, invertible sheaves
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 4 , July 2010 , pp. 964 - 998
Copyright
Copyright © Foundation Compositio Mathematica 2010

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