Tamagawa numbers on diagonal cubic surfaces, numerical evidence

1998/09/10 by Emmanuel Peyre, Yuri Tschinkel, Peyre, Emmanuel +1
Mathematics · #14G05 (Primary) 11G35 #14J45 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #msc:11G35 #msc:14G05 #msc:14J45

paper · pdf · doi:10.48550/arxiv.math/9809054

arxiv created 1998/09/10 · openalex publication_date 1998/09/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We test numerically the refined Manin's conjecture about the asymptotics of points of bounded height on Fano varieties for some diagonal cubic surfaces.

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• Tamagawa numbers of diagonal cubic surfaces of higher rank
• On a certain non-split cubic surface
• On Manin's conjecture for a certain singular cubic surface
• Manin's conjecture for a certain singular cubic surface
• Manin's conjecture for a class of singular cubic hypersurfaces