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Rational points and non-anticanonical height functions


Authors: Christopher Frei and Daniel Loughran
Journal: Proc. Amer. Math. Soc. 147 (2019), 3209-3223
MSC (2010): Primary 11D45; Secondary 14G05, 11G35
DOI: https://doi.org/10.1090/proc/14248
Published electronically: April 18, 2019
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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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Additional Information

Christopher Frei
Affiliation: School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
Email: christopher.frei@manchester.ac.uk

Daniel Loughran
Affiliation: School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
Email: daniel.loughran@manchester.ac.uk

DOI: https://doi.org/10.1090/proc/14248
Received by editor(s): February 2, 2018
Received by editor(s) in revised form: May 16, 2018
Published electronically: April 18, 2019
Communicated by: Rachel Pries
Article copyright: © Copyright 2019 American Mathematical Society