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 with partial corestriction upon a suitable choice of parameters, which generalizes a construction due to Mumford.

中文翻译：

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小Unit秩Shimura曲线的Oort猜想

我们证明，只要其规范的希格斯束中的单位部分的秩满足数值上限，则开放式Torelli轨迹通常不包含Siegel模块化品种中的Shimura曲线。作为一个应用，我们表明，科尔曼-奥尔特猜想成立时的参数的适当选择，从而推广由于芒福德的结构与部分相关联corestriction志村曲线。