Rational Points and Non-anticanonical Height Functions

Christopher Frei; Daniel Loughran

doi:10.1090/proc/14248

Rational Points and Non-anticanonical Height Functions

Christopher Frei, Daniel Loughran

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	1-17
Number of pages	17
Journal	Proceedings of the American Mathematical Society
DOIs	https://doi.org/10.1090/proc/14248
Publication status	Published - 2019

Access to Document

10.1090/proc/14248

Cite this

@article{9852b2db2f2f48e298d09695ddbf5e90,

title = "Rational Points and Non-anticanonical Height Functions",

abstract = "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.",

author = "Christopher Frei and Daniel Loughran",

year = "2019",

doi = "10.1090/proc/14248",

language = "English",

pages = "1--17",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

}

TY - JOUR

T1 - Rational Points and Non-anticanonical Height Functions

AU - Frei, Christopher

AU - Loughran, Daniel

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

U2 - 10.1090/proc/14248

DO - 10.1090/proc/14248

M3 - Article

SN - 0002-9939

SP - 1

EP - 17

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

ER -