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arXiv · 1712.03674

The Oort conjecture for Shimura curves of small unitary rank

Ke Chen·Xin Lu·Kang Zuo
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Abstract

We prove that a Shimura curve in the Siegel modular variety is not generically contained in the open Torelli locus as long as the rank of unitary part in its canonical Higgs bundle satisfies a numerical upper bound. As an application we show that the Coleman-Oort conjecture holds for Shimura curves associated to partial corestriction upon a suitable choice of parameters, which generalizes a construction due to Mumford.

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Ke Chen, Xin Lu, Kang Zuo. 2017-12-11. The Oort conjecture for Shimura curves of small unitary rank. https://arxiv.org/abs/1712.03674

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