Non-existence of Shimura curves of Mumford type generically in the non-hyperelliptic locus

Abstract

We show that there does not exist any Shimura curve with strictly maximal Higgs field generically in the Torelli locus of non-hyperelliptic curves of genus $g\ge 4$. In particular, Shimura curves of Mumford type are not generically in the Torelli locus of non-hyperelliptic curves of genus $g\ge 4$.

there is a gap in the proof of Theorem 3.1