2008/02/06 by Bogdan G. Vioreanu, Vioreanu, Bogdan G.
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.0802.0742
openalex publication_date 2008/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let V be a plane smooth cubic curve over a finitely generated field k. The Mordell-Weil theorem for V states that there is a finite subset P ⊂ V(k) such that the whole V(k) can be obtained from P by drawing secants and tangents through pairs of previously constructed points and consecutively adding their new intersection points with V. In this paper we present numerical data regarding the analogous statement for cubic surfaces. For the surfaces examined, we also test Manin's conjecture relating the asymptotics of rational points of bounded height on a Fano variety with the rank of the Picard group of the surface.