Counting integral points on universal torsors

2008/10/22 by Ulrich Derenthal, Derenthal, Ulrich · 2 citations
Computer Science · #11G35 (Primary) 11D45 #14G05 (Secondary) #Algebraic Geometry (math.AG) #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic, programming, and type systems #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0810.4122

openalex publication_date 2008/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Manin's conjecture for the asymptotic behavior of the number of rational points of bounded height on del Pezzo surfaces can be approached through universal torsors. We prove several auxiliary results for the estimation of the number of integral points in certain regions on universal torsors. As an application, we prove Manin's conjecture for a singular quartic del Pezzo surface.

Citations

• Rational points of bounded height on Fano varieties
• Manin's conjecture for a cubic surface with D₅ singularity

Cited by

• Iitaka fibrations and integral points: a family of arbitrarily polarized spherical threefolds
• Points of bounded height on quintic del Pezzo surfaces over the rational numbers

Related

• Universal torsors over Del Pezzo surfaces and rational points
• Counting imaginary quadratic points via universal torsors
• O-minimality on twisted universal torsors and Manin's conjecture over number fields
• The split torsor method for Manin's conjecture
• Integral Points on a del Pezzo Surface over Imaginary Quadratic Fields