Cones of orthogonal Shimura subvarieties and equidistribution

Let X be an orthogonal Shimura variety, and let Cᵣᵒʳᵗ(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 Cᵣᵒʳᵗ(X) for large values of r. They accumulate towards rays generated by wedge products of the Kähler class of X and the fundamental class of an orthogonal Shimura subvariety. We also compare Cᵣᵒʳᵗ(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.