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arXiv · 2208.07745

Cones of orthogonal Shimura subvarieties and equidistribution

Riccardo Zuffetti
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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.

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Riccardo Zuffetti. 2022-08-16. Cones of orthogonal Shimura subvarieties and equidistribution. https://arxiv.org/abs/2208.07745

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