Rational points and non-anticanonical height functions

Frei, Christopher; Loughran, Daniel

doi:10.1090/proc/14248

Rational points and non-anticanonical height functions
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by Christopher Frei and Daniel Loughran PDF

Proc. Amer. Math. Soc. 147 (2019), 3209-3223 Request permission

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.

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