On the Existence of Shimura curves in the Prym locus of abelian covers of projective line
| Autor: | Mohajer, Abolfazl |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Using the theory of Higgs bundles and their stabitlity properties associated to fibered surfaces and the Viehweg-Zuo characterization of Shimura curves in the moduli space of abelian varieties in terms of Higgs bundles, we prove that there does not exist any non-compact Shimura curves in the Prym locus of totally ramified $\Z_{2p}$- or $\Z_{2p}\times (\Z_{p})^{m-1}$-covers of the projective line in $A_{g}$ for $g\geq 8$, where $p\geq 5$ is a prime number. Comment: Comments are welcome |
| Databáze: | arXiv |
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