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

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

2007-02-19

arxiv.org/abs/math/0702549v1

Mathematics

Number Theory

10 pages

Scientific paper

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 at least 3.

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