On a constant arising in Manin's conjecture for Del Pezzo surfaces

2007/02/19 by Ulrich Derenthal, Derenthal, Ulrich
Mathematics · #14G05 (Secondary) #14J26 (Primary) 52B05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.AG #math.NT #msc:14G05 #msc:14J26 #msc:52B05

paper · pdf · doi:10.48550/arxiv.math/0702549

10 pages

arxiv created 2007/02/19 · openalex publication_date 2007/02/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For split smooth Del Pezzo surfaces, we analyse the structure of the effective cone and prove a recursive formula for the value of alpha, appearing in the leading constant as predicted by Peyre of Manin's conjecture on the number of rational points of bounded height on the surface. Furthermore, we calculate alpha for all singular Del Pezzo surfaces of degree at least 3.

Citations

• An overview of Manin's conjecture for del Pezzo surfaces
• Rational points of bounded height on Fano varieties

Related

• An overview of Manin's conjecture for del Pezzo surfaces
• Points of bounded height on quintic del Pezzo surfaces over the rational numbers
• On Manin's conjecture for singular del Pezzo surfaces of degree four, I
• On the factor alpha in Peyre's constant
• Manin's conjecture for a quintic del Pezzo surface with A₂ singularity