Equidistribution and freeness on Grassmannians

Browning, Tim; Horesh, Tal; Wilsch, Florian

doi:10.2140/ant.2022.16.2385

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Equidistribution and freeness on Grassmannians

Tim Browning, Tal Horesh and Florian Wilsch

Vol. 16 (2022), No. 10, 2385–2407

DOI: 10.2140/ant.2022.16.2385

Abstract

We associate a certain tensor product lattice to any primitive integer lattice and ask about its typical shape. These lattices are related to the tangent bundle of Grassmannians and their study is motivated by Peyre’s program on “freeness” for rational points of bounded height on Fano varieties.

Keywords

Manin conjecture, freeness, Grassmannian, equidistribution, lattice

Mathematical Subject Classification

Primary: 14G05

Secondary: 11N45, 11P21, 14M15, 20G20

Milestones

Received: 11 June 2021

Revised: 20 November 2021

Accepted: 1 February 2022

Published: 28 January 2023

Authors

Tim Browning
IST Austria Klosterneuburg Austria

Tal Horesh
IST Austria Klosterneuburg Austria

Florian Wilsch
IST Austria Klosterneuburg Austria

Vol. 16, No. 10, 2022