Proves algebraic hyperbolicity and big Picard theorems for Kähler manifolds with zero-dimensional period maps from polarized VHS, plus hyperbolicity and general type properties for their compactifications.
Moduli of canonically polarized manifolds, higher order Kodaira-Spencer maps, and an analogy to Calabi-Yau manifolds
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abstract
A Finsler metric, whose holomorphic curvature is bounded from above by a negative constant, is constructed on the moduli stack of canonically polarized manifolds including singularities. Demailly's version of Ahlfors' lemma yields hyperbolicity of the moduli stack.
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2020 1verdicts
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Big Picard theorems and algebraic hyperbolicity for varieties admitting a variation of Hodge structures
Proves algebraic hyperbolicity and big Picard theorems for Kähler manifolds with zero-dimensional period maps from polarized VHS, plus hyperbolicity and general type properties for their compactifications.