Mathematical Research Letters

Volume 14 (2007)

Number 3

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

Pages: 481 – 489

DOI: http://dx.doi.org/10.4310/MRL.2007.v14.n3.a12

Author

Ulrich Derenthal (Universität Zürich)

Abstract

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 $\ge 3$.

Full Text (PDF format)