Height of rational points on random Fano hypersurfaces

2020/06/03 by Pierre Le Boudec, Boudec, Pierre Le
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2006.02288

openalex publication_date 2020/06/03 · openalex created_date 2020/06/12 · openalex updated_date 2026/07/28

Abstract

We investigate in a statistical fashion the smallest height of a rational point on a Fano hypersurface defined over the field of rational numbers. Along the way, we establish an average version of Manin's conjecture about the number of rational points of bounded height on Fano varieties for the complete family of Fano hypersurfaces of fixed degree and dimension.

Related

• Distribution of rational points on random Fano hypersurfaces
• Rational points on some Fano cubic bundles
• On K-stability, height bounds and the Manin-Peyre conjecture
• Sharp bounds on the height of K-semistable Fano varieties II, the log case
• Freeness alone is insufficient for Manin-Peyre