Height of rational points on random Fano hypersurfaces

Le Boudec, Pierre

doi:10.2140/ant.2021.15.657

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Height of rational points on random Fano hypersurfaces

Pierre Le Boudec

Vol. 15 (2021), No. 3, 657–672

DOI: 10.2140/ant.2021.15.657

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.

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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

Vol. 15, No. 3, 2021