15 citations · 44 across the 10 of their papers we have counts for
Showing 2006Show all
3 papers · 1 filter
math.NT2006
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…
math.AG2006
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))…
math.AG2006★ 15 cited
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…