Rational Points and Non-anticanonical Height Functions

Christopher Frei, Daniel Loughran

Research output: Contribution to journalArticlepeer-review


A conjecture of Batyrev and Manin predicts the asymptotic behaviourof rational points of bounded height on smooth projective varieties overnumber fields. We prove some new cases of this conjecture for conic bundle surfacesequipped with some non-anticanonical height functions. As a special case,we verify these conjectures for the first time for some smooth cubic surfaces forheight functions associated to certain ample line bundles.
Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalProceedings of the American Mathematical Society
Publication statusPublished - 2019

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