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arXiv · 1601.07514

Hyperbolicity of cyclic covers and complements

Yuchen Liu
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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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Yuchen Liu. 2016-01-27. Hyperbolicity of cyclic covers and complements. https://doi.org/10.1090/tran/7097

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