Hyperbolicity of cyclic covers and complements

Liu, Yuchen

doi:10.1090/tran/7097

Hyperbolicity of cyclic covers and complements
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by Yuchen Liu PDF

Trans. Amer. Math. Soc. 370 (2018), 5341-5357 Request permission

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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