Singular del Pezzo surfaces whose universal torsors are hypersurfaces

By Ulrich Derenthal. 2006

98 citations recorded by the source corpus.

We classify all generalized del Pezzo surfaces (that is, minimal desingularizations of singular del Pezzo surfaces containing only rational double points) whose universal torsors are open subsets of hypersurfaces in affine space. Equivalently, their Cox rings are polynomial rings with exactly one relation. For all 30 types with this property, we describe the Cox rings in detail.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/61751a2974f43e4662cd9a562191fb60bfbb422b

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

On Cox rings of K3 surfaces (2009, background): “and its multigrading can be explicitly determined in terms of a deﬁning fan, see [8]. Moreover, for del Pezzo surfaces X there are recent results on generators and relations of the Cox ring, see [5], [9], [14], [25], [26], and [27]. In the present paper, we investigate Cox rings of K3-surfaces X, i.”
The Cox ring of an algebraic variety with torus action (2009, methodology): “As the intersection graphs of their resolutions are known, see [1], the methods just outlined provide Cox rings of (possibly singular) Gorenstein del Pezzo Ksurfaces X ; note that Derenthal computed in [8] the Cox rings of the minimal resolutions X̃ without assuming existence of a K-action for the c”