Mathematical Research Letters

Volume 14 (2007)

Number 3

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

Pages: 481 – 489



Ulrich Derenthal (Universität Zürich)


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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