Vol. 15, No. 3, 2021

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Height of rational points on random Fano hypersurfaces

Pierre Le Boudec

Vol. 15 (2021), No. 3, 657–672
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.

Keywords
Fano hypersurfaces, rational points, heights
Mathematical Subject Classification 2010
Primary: 11D45
Secondary: 11G50, 14G05
Milestones
Received: 18 July 2019
Revised: 7 January 2020
Accepted: 6 February 2020
Published: 20 May 2021
Authors
Pierre Le Boudec
Departement Mathematik und Informatik, Fachbereich Mathematik
Universitaet Basel
Basel
Switzerland