Manin's conjecture for a singular quartic del Pezzo surface

Details Manin's conjecture for a singular quartic del Pezzo surface Manin's conjecture for a singular quartic del Pezzo surface

2011-09-28

arxiv.org/abs/1109.6253v1

Mathematics

Number Theory

Scientific paper

We prove Manin's conjecture for a split singular quartic del Pezzo surface
with singularity type $2\Aone$ and eight lines. This is achieved by equipping
the surface with a conic bundle structure. To handle the sum over the family of
conics, we prove a result of independent interest on a certain restricted
divisor problem for four binary linear forms.

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