On the Existence of Shimura curves in the Prym locus of abelian covers of projective line

Abolfazl Mohajer

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arXiv · 2408.10219

On the Existence of Shimura curves in the Prym locus of abelian covers of projective line

Abolfazl Mohajer

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Abstract

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.

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BibTeX RIS

Abolfazl Mohajer. 2024-07-25. On the Existence of Shimura curves in the Prym locus of abelian covers of projective line. https://arxiv.org/abs/2408.10219

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