Equidistribution and freeness on Grassmannians
Tim Browning, Tal Horesh, Florian Wilsch
TL;DR
This paper investigates the typical geometric structure of tensor product lattices linked to tangent bundles of Grassmannians, motivated by Peyre's freeness concept for rational points on Fano varieties.
Contribution
It introduces a new lattice construction associated with Grassmannians and explores its shape, connecting lattice theory with algebraic geometry and rational point distribution.
Findings
Lattice structures relate to tangent bundles of Grassmannians
Insights into Peyre's freeness for rational points
Potential applications to Fano varieties
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 programme on "freeness" for rational points of bounded height on Fano varieties.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds