Cones of orthogonal Shimura subvarieties and equidistribution

Let X be an orthogonal Shimura variety, and let Cᵒʳᵗᵣ(X) C r ort ( 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 Cᵒʳᵗᵣ(X) C r ort ( 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 Cᵒʳᵗᵣ(X) C r ort ( 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.