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The Oort conjecture for Shimura curves of small unitary rank

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 Added by Xin Lu
 Publication date 2017
  fields
and research's language is English




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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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