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Manin's conjecture for a certain singular cubic surface

Ulrich Derenthal
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Abstract

We prove Manin's conjecture for a singular cubic surface S with a singularity of type E6. If U is the open subset of S obtained by deleting the unique line from S, then the number of rational points in U with anticanonical height bounded by B behaves asymptotically as cB(log B)^6, where the constant c agrees with the one conjectured by Peyre.

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Ulrich Derenthal. 2005-04-01. Manin's conjecture for a certain singular cubic surface. https://arxiv.org/abs/math/0504016

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