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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 ₂- or ₂ () ^m-1-covers of the projective line in A₆ for g 8, where p 5 is a prime number.
Abolfazl Mohajer (Thu,) studied this question.
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