On Shimura curves generated by families of Galois G-covers of curves.

In this paper we prove that there are no families of cyclic Z n -covers of elliptic curves which generate non-compact Shimura (special) curves that lie generically in the Torelli locus T g of abelian varieties with g ≥ 8 when n has a proper prime factor p ≥ 7. This non-existence is also shown for families of Z n -covers of curves of any genus s provided that n has a large enough prime factor p (depending on s). We achieve these results by applying the theory of Higgs bundles and the Viehweg-Zuo characterization of Shimura curves in the moduli space of principally polarized abelian varieties. [ABSTRACT FROM AUTHOR]