The Cox ring of a K3 surface with Picard number two

Details The Cox ring of a K3 surface with Picard number two The Cox ring of a K3 surface with Picard number two

2009-09-28

arxiv.org/abs/0909.5121v1

Mathematics

Algebraic Geometry

12 Pages, 1 figure

Scientific paper

We study generators and relations for Cox rings of K3 surfaces of Picard number 2. The main results are explicit descriptions of the Cox rings when X is a double cover of P^2 ramified over a sextic with a tritangent, a quartic surface in P^3 with a line or a K3 surface with intersection matrix $\begin{pmatrix}0 & d d & 0 \end{pmatrix}$. This note can be seen as an addendum to a recent paper by Artebani, Hausen and Laface.

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