Singular del Pezzo surfaces whose universal torsors are hypersurfaces
Singular del Pezzo surfaces whose universal torsors are hypersurfaces
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, …