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Counting rational points of bounded non-anticanonical height

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Speaker: 
Christopher Frei
Affiliation: 
University of Manchester
Date: 
Wed, 2018-03-28 17:00 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

A conjecture of Batyrev and Manin predicts the asymptotic behaviour of rational points of bounded height on smooth projective varieties over number fields. We discuss some new cases of this conjecture for conic bundle surfaces equipped with certain non-anticanonical height functions. As a special case, the conjecture is verified for the first time for some smooth cubic surfaces with height functions associated to some ample line bundles. This is joint work with Dan Loughran.

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