The density of rational points on a certain singular cubic surface

2004/04/13 by T. D. Browning, Browning, T. D.
Mathematics · #11G35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0404245

openalex publication_date 2004/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the number of non-trivial rational points of height at most B, that lie on the cubic surface x₁x₂x₃=x₄(x₁+x₂+x₃)², has order of magnitude B(log B)⁶. This agrees with the Manin conjecture.

Citations

• Rational points of bounded height on Fano varieties

Related

• The density of rational points on Cayley's cubic surface
• Rational Points on the Fermat Cubic Surface
• On Manin's conjecture for a certain singular cubic surface
• On a certain non-split cubic surface
• Manin's conjecture for a class of singular cubic hypersurfaces