Antonio Laface

Learn More
Different choices of basis yield (non-canonically) isomorphic Cox rings and any of them is a “total” coordinate ring for X in the sense that, (1) The homogeneous coordinate rings ⊕∞ s=0H (X, sD) of all images of X via complete linear systems φD : X → P(H(X,D)) are subalgebras of Cox(X). (2) If the Cox ring is a finitely generated k-algebra then X can be(More)
We study Cox rings of K3-surfaces. A first result is that a K3surface 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(More)