Coarse moduli spaces of canonically polarized and polarized Calabi-Yau manifolds are Kobayashi V-hyperbolic, which implies Campana-type isotriviality over hyperbolically special bases.
168, Cambridge University Press, Cambridge, 2017, Second edition of [ MR2012297]
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Hyperbolicity of coarse moduli spaces and isotriviality for certain families
Coarse moduli spaces of canonically polarized and polarized Calabi-Yau manifolds are Kobayashi V-hyperbolic, which implies Campana-type isotriviality over hyperbolically special bases.