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Equidistribution and freeness on Grassmannians

Tim Browning, Tal Horesh and Florian Wilsch

Vol. 16 (2022), No. 10, 2385–2407
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