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arXiv · 2403.06217

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

Xin Lu·Shengli Tan·Kang Zuo
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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 $g\geq 4$. In particular, Shimura curves of Mumford type are not generically in the Torelli locus of non-hyperelliptic curves of genus $g\geq 4$.

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Xin Lu, Shengli Tan, Kang Zuo. 2024-03-10. Non-existence of Shimura curves of Mumford type generically in the non-hyperelliptic locus. https://arxiv.org/abs/2403.06217

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