• Corpus ID: 232014584

Equidistribution and freeness on Grassmannians

@inproceedings{Browning2021EquidistributionAF,
  title={Equidistribution and freeness on Grassmannians},
  author={Tim D. Browning and Tal Horesh and Florian Wilsch},
  year={2021}
}
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. 
Counting flags of primitive lattices
We count flags of primitive lattices, which are objects of the form {0} = Λ(0) < Λ(1) < · · · < Λ(`) = Zn, where every Λ(i) is a primitive lattice in Zn. The counting is with respect to two different
Equidistribution of primitive lattices in $\mathbb{R}^n$
TLDR
This work adds to a prior work of Schmidt by allowing sets that are general enough in the spaces of parameters to conclude joint equidistribution of these parameters, e.g., the shapes of primitive lattices, and the shape of their orthogonal lattices.

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