Rational points of bounded height on general conic bundle surfaces

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 or 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.

35 pages; final version

References in corpus (1)

• Generalised divisor sums of binary forms over number fields

Cited by in corpus (7)

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• Rational points on del Pezzo surfaces of degree four
• Counting rational points on quartic del Pezzo surfaces with a rational conic
• On upper bounds of Manin type
• Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4
• Integral points on symmetric affine cubic surfaces
• The geometric exceptional set in Manin's conjecture for Batyrev and Tschinkel's example