Hyperbolicity of varieties supporting a variation of Hodge structure

  title={Hyperbolicity of varieties supporting a variation of Hodge structure},
  author={Yohan Brunebarbe and Beno{\^i}t Cadorel},
  journal={arXiv: Algebraic Geometry},
We generalize former results of Zuo and the first author showing some hyperbolicity properties of varieties supporting a variation of Hodge structure. Our proof only uses the special curvature properties of period domains. In particular, in contrast to the former approaches, it does not use any result on the asymptotic behaviour of the Hodge metric. 

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