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- W2997757883 abstract "Consider a smooth projective family of complex polarized manifolds with semi-ample canonical sheaf over a quasi-projective manifold $V$. When the associated moduli map $Vto P_h$ from the base to coarse moduli space is quasi-finite, we prove that the generalized big Picard theorem holds for the base manifold $V$: for any projective compactification $Y$ of $V$, any holomorphic map $f:Delta-{0}to V$ from the punctured unit disk to $V$ extends to a holomorphic map of the unit disk $Delta$ into $Y$. This result generalizes our previous work on the Brody hyperbolicity of $V$ (i.e. there are no entire curves on $V$), as well as a more recent work by Lu-Sun-Zuo on the Borel hyperbolicity of $V$ (i.e. any holomorphic map from a quasi-projective variety to $V$ is algebraic). We also obtain generalized big Picard theorem for bases of log Calabi-Yau families." @default.
- W2997757883 created "2020-01-10" @default.
- W2997757883 creator A5060224666 @default.
- W2997757883 date "2019-12-24" @default.
- W2997757883 modified "2023-09-25" @default.
- W2997757883 title "Big Picard theorem for moduli spaces of polarized manifolds" @default.
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- W2997757883 doi "https://doi.org/10.48550/arxiv.1912.11442" @default.
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