On Higgs bundles over Shimura varieties of ball quotient type
  We prove the generic exclusion of certain Shimura varieties of unitary and orthogonal types from the Torelli locus. The proof relies on a slope inequality on surface fibration due to G. Xiao, and the main result implies that certain Shimura varieties only meet the Torelli locus in dimension zero. 
Ke Chen, Xin Lu, Sheng-Li Tan, Kang Zuo
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