On a certain non-split cubic surface

Régis de la Bretèche; Kevin Destagnol; Jianya Liu; Jie Wu; Yongqiang Zhao

On a certain non-split cubic surface

Number Theory 2018-12-13 v2

Authors: Régis de la Bretèche , Kevin Destagnol , Jianya Liu , Jie Wu , Yongqiang Zhao

Abstract

In this note, we establish an asymptotic formula for the number of rational points of bounded height on the singular cubic surface $x_0(x_1^2 + x_2^2)=x_3^3$ with a power-saving error term, which verifies the Manin-Peyre conjectures for this surface.

Keywords

cubic fourfolds rational points on curves canonical height

Cite

@article{arxiv.1709.09476,
  title  = {On a certain non-split cubic surface},
  author = {Régis de la Bretèche and Kevin Destagnol and Jianya Liu and Jie Wu and Yongqiang Zhao},
  journal= {arXiv preprint arXiv:1709.09476},
  year   = {2018}
}

Comments

v2. 18 pages, one author added

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