Hyperbolicity of cyclic covers and complements

Yuchen Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 ℙn+1that are cyclic covers of ℙn.

Original languageEnglish (US)
Pages (from-to)5341-5357
Number of pages17
JournalTransactions of the American Mathematical Society
Issue number8
StatePublished - 2018
Externally publishedYes


  • Brody hyperbolicity
  • Cyclic covers
  • Hypersurfaces

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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