Mathematical Research Letters
Volume 14 (2007)
On a constant arising in Manin’s conjecture for Del Pezzo surfaces
Pages: 481 – 489
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 $\ge 3$.