35 citations · 129 across the 34 of their papers we have counts for
4 papers · 1 filter
Universal torsors over Del Pezzo surfaces and rational points
Ulrich Derenthal, Yuri Tschinkel
We discuss Manin's conjecture concerning the distribution of rational points of bounded height on Del Pezzo surfaces, and its refinement by Peyre, and explain applications of unive…
Universal torsors of Del Pezzo surfaces and homogeneous spaces
Ulrich Derenthal
Let Cox(S) be the homogeneous coordinate ring of the blow-up S of P^2 in r general points, i.e., a smooth Del Pezzo surface of degree 9-r. We prove that for r=6 and 7, Proj(Cox(S))…
Singular del Pezzo surfaces whose universal torsors are hypersurfaces
Ulrich Derenthal
We classify all generalized del Pezzo surfaces (i.e., minimal desingularizations of singular del Pezzo surfaces containing only rational double points) whose universal torsors are…
On the Cox ring of Del Pezzo surfaces
Ulrich Derenthal
Let S_r be the blow-up of P^2 in r general points, i.e., a smooth Del Pezzo surface of degree 9-r. For r <= 7, we determine the quadratic equations defining its Cox ring explicitly…