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arXiv · 1109.6253

Manin's conjecture for a singular quartic del Pezzo surface

Daniel Loughran
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Abstract

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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Daniel Loughran. 2013-02-01. Manin's conjecture for a singular quartic del Pezzo surface. https://doi.org/10.1112/jlms%2Fjds017

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