### Abstract

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

*Proceedings of the American Mathematical Society*,

*147*(8), 3209-3223. https://doi.org/10.1090/proc/2019-147-08

**Rational points and non-anticanonical height functions.** / Frei, Christopher; Loughran, Daniel.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 147, no. 8, pp. 3209-3223. https://doi.org/10.1090/proc/2019-147-08

}

TY - JOUR

T1 - Rational points and non-anticanonical height functions

AU - Frei, Christopher

AU - Loughran, Daniel

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

U2 - 10.1090/proc/2019-147-08

DO - 10.1090/proc/2019-147-08

M3 - Article

VL - 147

SP - 3209

EP - 3223

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 8

ER -