Mathematical Research Letters

Volume 14, Issue 3, May 2007 pp. 481-489.

On a constant arising in Manin's conjecture for Del Pezzo surfaces

Authors: Ulrich Derenthal
Author institution: Universität Zürich

Summary: For split smooth Del Pezzo surfaces, we analyse the structure of the effective cone and prove a recursive formula for the value of $\alpha$, appearing in the leading constant as predicted by Peyre of Manin's conjecture on the number of rational points of bounded height on the surface. Furthermore, we calculate $\alpha$ for all singular Del Pezzo surfaces of degree $\ge 3$.

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