Points of bounded height on quintic del Pezzo surfaces over number fields

authored by

Christian Bernert, Ulrich Derenthal

Abstract

We prove Manin's conjecture for split smooth quintic del Pezzo surfaces over arbitrary number fields with respect to fairly general anticanonical height functions. After passing to universal torsors, we first show that we may restrict the torsor variables to their typical sizes, and then we can solve the counting problem in the framework of o-minimal structures.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Preprint

Publication date

30.05.2024

Publication status

E-pub ahead of print

Electronic version(s)

https://doi.org/10.48550/arXiv.2405.20293 (Access: Open)