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Hyperbolicity of varieties supporting a variation of Hodge structure

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arxiv 1707.01327 v1 pith:ACVMZZYV submitted 2017-07-05 math.AG math.CV

Yohan Brunebarbe , Benoit Cadorel This is my paper · ORCID
classification math.AGmath.CV
keywords hodgeformerhyperbolicitypropertiesstructuresupportingvariationvarieties
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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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  1. Hyperbolicity of coarse moduli spaces and isotriviality for certain families

    math.AG 2019-08 conditional novelty 7.0 of 10

    Coarse moduli spaces of canonically polarized and polarized Calabi-Yau manifolds are Kobayashi V-hyperbolic, which implies Campana-type isotriviality over hyperbolically special bases.

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