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.
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 language | English |
|---|---|
| Pages (from-to) | 1-17 |
| Number of pages | 17 |
| Journal | Proceedings of the American Mathematical Society |
| Early online date | 18 Apr 2019 |
| DOIs | |
| Publication status | Published - 2019 |