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

2024/07/25 by Abolfazl Mohajer, Mohajer, Abolfazl
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2408.10219

openalex publication_date 2024/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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× (\Z_p)^m-1-covers of the projective line in A_g for g≥ 8, where p≥ 5 is a prime number.

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