Michela Artebani, Juergen Hausen, Antonio Laface
Published 2009-01-04, updated 2009-09-03Version 3
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 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.
Comments: minor corrections, to appear in Compositio Mathematica, 32 pages
Journal: Compos. Math. 146 (2010), no. 4, 964-998
Counting Zariski chambers on Del Pezzo surfaces
Nef cone volumes and discriminants of abelian surfaces
Classification of Fano 4-folds with Lefschetz defect 3 and Picard number 5
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