Cones of orthogonal Shimura subvarieties and equidistribution
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929405114187776 |
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| author | Zuffetti, Riccardo |
| author_facet | Zuffetti, Riccardo |
| contents | 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 Kähler 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_07745 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Cones of orthogonal Shimura subvarieties and equidistribution Zuffetti, Riccardo Algebraic Geometry Number Theory 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 Kähler 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. |
| title | Cones of orthogonal Shimura subvarieties and equidistribution |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2208.07745 |