On the factor alpha in Peyre's constant

2012/02/28 by Ulrich Derenthal, Derenthal, Ulrich, Andreas-Stephan Elsenhans +3
Mathematics · #14G05 (Secondary) #14J26 (Primary) 51M20 #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:51M20

paper · pdf · doi:10.48550/arxiv.1202.6287

11 pages, 1 figure

openalex publication_date 2012/02/28 · arxiv created 2013/02/01 · arxiv updated 2013/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an arbitrary del Pezzo surface S, we compute alpha(S), which is the volume of a certain polytope in the dual of the effective cone of S, using Magma and Polymake. The constant alpha(S) appears in Peyre's conjecture for the leading term in the asymptotic formula for the number of rational points of bounded height on S over number fields.

Citations

• Rational points of bounded height on Fano varieties

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