Abstract
AbstractLet X be an orthogonal Shimura variety, and let $$\mathcal {C}^{\textrm{ort}}_{r}(X)$$
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 $$\mathcal {C}^{\textrm{ort}}_{r}(X)$$
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 $$\mathcal {C}^{\textrm{ort}}_{r}(X)$$
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.
Funder
Technische Universität Darmstadt
Publisher
Springer Science and Business Media LLC