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

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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Published 1 January 2007