Cones of orthogonal Shimura subvarieties and equidistribution
Algebraic Geometry
2024-07-03 v2 Number Theory
Abstract
Let X be an orthogonal Shimura variety, and let C_r(X) be the cone generated by the cohomology classes of orthogonal Shimura subvarieties in X of dimension r. We investigate the asymptotic properties of the generating rays of C_r(X) for large values of r. They accumulate towards rays generated by wedge products of the K\"ahler class of X and the fundamental class of an orthogonal Shimura subvariety. We also compare C_r(X) with the cone generated by the special cycles of dimension r. The main ingredient to achieve the results above is the equidistribution of orthogonal Shimura subvarieties.
Keywords
Cite
@article{arxiv.2208.07745,
title = {Cones of orthogonal Shimura subvarieties and equidistribution},
author = {Riccardo Zuffetti},
journal= {arXiv preprint arXiv:2208.07745},
year = {2024}
}
Comments
16 pages, article shortened, typos corrected, main results unchanged. To appear in Manuscripta Mathematica