On Peyre's constant alpha for del Pezzo surfaces

Details On Peyre's constant alpha for del Pezzo surfaces On Peyre's constant alpha for del Pezzo surfaces

2012-02-28

arxiv.org/abs/1202.6287v1

Mathematics

Algebraic Geometry

15 pages, 1 figure

Scientific paper

For an arbitrary del Pezzo surface S, we compute Peyre's constant alpha(S),
which is the volume of a certain polytope in the dual of the effective cone of
S, using Magma and Polymake. Peyre conjectured that alpha(S) appears in the
asymptotic formula for the number of rational points of bounded height on S
over number fields.

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