## Abstract

A conjecture of Manin predicts the asymptotic distribution of rational points of

bounded height on Fano varieties. In this paper we use conic bundles to obtain correct lower bounds for a wide class of surfaces over number fields for which the conjecture is still far from being proved. For example, we obtain the conjectured lower bound of Manin's conjecture for any del Pezzo surface whose Picard rank is sfficiently large, or for arbitrary del Pezzo surfaces after possibly an extension of the ground field of small degree.

bounded height on Fano varieties. In this paper we use conic bundles to obtain correct lower bounds for a wide class of surfaces over number fields for which the conjecture is still far from being proved. For example, we obtain the conjectured lower bound of Manin's conjecture for any del Pezzo surface whose Picard rank is sfficiently large, or for arbitrary del Pezzo surfaces after possibly an extension of the ground field of small degree.

Original language | English |
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Pages (from-to) | 407-440 |

Journal | Proceedings of the London Mathematical Society |

Volume | 117 |

Issue number | 2 |

Early online date | 3 Apr 2018 |

DOIs | |

Publication status | Published - Aug 2018 |