Rational points of bounded height on general conic bundle surfaces

Frei, C., Loughran, D. and Sofos, E. (2018) Rational points of bounded height on general conic bundle surfaces. Proceedings of the London Mathematical Society, 117(2), pp. 407-440. (doi: 10.1112/plms.12134)

Abstract

A conjecture of Manin predicts the asymptotic distribution of rational points of bounded height on Fano varieties. In this paper we use conic bundles to obtain correct lower bounds for a wide class of surfaces over number fields for which the conjecture is still far from being proved. For example, we obtain the conjectured lower bound of Manin's conjecture for any del Pezzo surface whose Picard rank is sufficiently large, or for arbitrary del Pezzo surfaces after possibly an extension of the ground field of small degree.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Sofos, Dr Efthymios
• Authors: Frei, C., Loughran, D., and Sofos, E.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Proceedings of the London Mathematical Society
• Publisher: London Mathematical Society
• ISSN: 0024-6115
• ISSN (Online): 1460-244X
• Published Online: 03 April 2018
• Copyright Holders: Copyright © 2018 London Mathematical Society
• First Published: First published in Proceedings of the London Mathematical Society 117(2): 407-440
• Publisher Policy: Reproduced in accordance with the publisher copyright policy