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

2024/05/30 by Christian Bernert, Ulrich Derenthal, Bernert, Christian +1 · 1 citation
Mathematics · #11G35 (Primary) 11D45 #14G05 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2405.20293

openalex publication_date 2024/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• The spaces of rational curves on del Pezzo surfaces via conic bundles

Related

• Points of bounded height on quintic del Pezzo surfaces over the rational numbers
• The split torsor method for Manin's conjecture
• Universal torsors over Del Pezzo surfaces and rational points
• Integral points of bounded height on quintic del Pezzo surfaces over number fields
• Equidistribution and the torsor method