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 with partial corestriction upon a suitable choice of parameters, which generalizes a construction due to Mumford.
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This work is supported by SFB/Transregio 45 Periods, Moduli Spaces and Arithmetic of Algebraic Varieties of DFG, by NSF of China Grant Nos. 11771203, 11231003, 11301495, Fundamental Research Funds for the Central Universities, Nanjing University, No. 0203-14380009, and by the Science Foundation of Shanghai (No. 13DZ2260400).
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Chen, K., Lu, X. & Zuo, K. The Oort Conjecture for Shimura Curves of Small Unitary Rank. Commun. Math. Stat. 6, 249–268 (2018). https://doi.org/10.1007/s40304-018-0155-8
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DOI: https://doi.org/10.1007/s40304-018-0155-8