Rational points and non-anticanonical height functions

Christopher Frei, Daniel Loughran

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)3209-3223
Number of pages15
JournalProceedings of the American Mathematical Society
Volume147
Issue number8
Early online date18 Apr 2019
DOIs
Publication statusPublished - 2019

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