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Hyperbolicity of cyclic covers and complements


Author: Yuchen Liu
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 32Q45; Secondary 14J70, 14J29
DOI: https://doi.org/10.1090/tran/7097
Published electronically: December 29, 2017
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Abstract: We prove that a cyclic cover of a smooth complex projective variety is Brody hyperbolic if its branch divisor is a generic small deformation of a large enough multiple of a Brody hyperbolic base-point-free ample divisor. We also show the hyperbolicity of complements of those branch divisors. As an application, we find new examples of Brody hyperbolic hypersurfaces in $ \mathbb{P}^{n+1}$ that are cyclic covers of $ \mathbb{P}^n$.


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Additional Information

Yuchen Liu
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544-1000
Email: yuchenl@math.princeton.edu

DOI: https://doi.org/10.1090/tran/7097
Keywords: Brody hyperbolicity, cyclic covers, hypersurfaces
Received by editor(s): May 26, 2016
Received by editor(s) in revised form: October 13, 2016
Published electronically: December 29, 2017
Additional Notes: The author was partially supported by NSF grant DMS-0968337.
Article copyright: © Copyright 2017 American Mathematical Society

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