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.
Semi-positivity from Higgs bundles
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abstract
We prove a generalization of the Fujita-Kawamata-Zuo semi-positivity Theorem for filtered regular meromorphic Higgs bundles and tame harmonic bundles. Our approach gives a new proof in the cases already considered by these authors. We give also an application to the geometry of smooth quasi-projective complex varieties admitting a semisimple complex local system with infinite monodromy.
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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.