### Abstract

A conjecture of Batyrev and Manin predicts the asymptotic behaviour of rational points of bounded height on smooth projective varieties over number fields. We prove some new cases of this conjecture for conic bundle surfaces equipped with some non-anticanonical height functions. As a special case, we verify these conjectures for the first time for some smooth cubic surfaces for height functions associated to certain ample line bundles.

Original language | English |
---|---|

Pages (from-to) | 3209-3223 |

Number of pages | 15 |

Journal | Proceedings of the American Mathematical Society |

Volume | 147 |

Issue number | 8 |

Early online date | 18 Apr 2019 |

DOIs | |

Publication status | Published - 2019 |

## Cite this

Frei, C., & Loughran, D. (2019). Rational points and non-anticanonical height functions.

*Proceedings of the American Mathematical Society*,*147*(8), 3209-3223. https://doi.org/10.1090/proc/2019-147-08