On Cox rings of K3-surfaces

Details On Cox rings of K3-surfaces On Cox rings of K3-surfaces

2009-01-04

arxiv.org/abs/0901.0369v3

Compos. Math. 146 (2010), no. 4, 964-998

Mathematics

Algebraic Geometry

minor corrections, to appear in Compositio Mathematica, 32 pages

Scientific paper

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.

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