Rational points of bounded height on general conic bundle surfaces

Christopher Frei, Daniel Loughran, Efthymios Sofos

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    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.
    Original languageEnglish
    Pages (from-to)407-440
    JournalProceedings of the London Mathematical Society
    Volume117
    Issue number2
    Early online date3 Apr 2018
    DOIs
    Publication statusPublished - Aug 2018

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