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

2024/03/10 by Lu, Xin, Tan, Shengli, Zuo, Kang · 1 citation
#14E30 #14J10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.06217

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≥ 4. In particular, Shimura curves of Mumford type are not generically in the Torelli locus of non-hyperelliptic curves of genus g≥ 4.

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• Mumford-type Shimura curves contained in the Torelli locus

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