Planes in four space and four associated CM points
Number Theory
2021-06-22 v2 Dynamical Systems
Abstract
To any two-dimensional rational plane in four-dimensional space one can naturally attach a point in the Grassmannian Gr(2,4) and four lattices of rank two. Here, the first two lattices originate from the plane and its orthogonal complement and the second two essentially arise from the accidental local isomorphism between SO(4) and SO(3)xSO(3). As an application of a recent result of Einsiedler and Lindenstrauss on algebraicity of joinings we prove simultaneous equidistribution of all of these objects under two splitting conditions.
Cite
@article{arxiv.1901.05833,
title = {Planes in four space and four associated CM points},
author = {Menny Aka and Manfred Einsiedler and Andreas Wieser},
journal= {arXiv preprint arXiv:1901.05833},
year = {2021}
}
Comments
45 pages, added a section about oriented planes. To appear in Duke Mathematical Journal