Big Picard theorem and algebraic hyperbolicity for varieties admitting a variation of Hodge structures

16 Apr 2020 Deng Ya

In this paper we study three notions of hyperbolicity for varieties admitting complex polarized variation of Hodge structures ($\mathbb{C}$-PVHS for short). In the first part we prove that if a quasi-projective manifold $U$ admits a $\mathbb{C}$-PVHS whose period map is quasi-finite, then $U$ is algebraically hyperbolic in the sense of Demailly, and that the generalized big Picard theorem holds for $U$: any holomorphic map $f:\Delta-\{0\}\to U$ from the punctured unit disk to $U$ extends to a holomorphic map of the unit disk $\Delta$ into any projective compactification of $U$... (read more)

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