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arXiv · 0901.0369

On Cox rings of K3-surfaces

Michela Artebani·Juergen Hausen·Antonio Laface
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Abstract

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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Michela Artebani, Juergen Hausen, Antonio Laface. 2009-09-03. On Cox rings of K3-surfaces. https://doi.org/10.1112/s0010437x09004576

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