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 ℙn+1that are cyclic covers of ℙn.
Original language | English (US) |
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Pages (from-to) | 5341-5357 |
Number of pages | 17 |
Journal | Transactions of the American Mathematical Society |
Volume | 370 |
Issue number | 8 |
DOIs | |
State | Published - 2018 |
Funding
Received by the editors May 26, 2016, and, in revised form, October 13, 2016. 2010 Mathematics Subject Classification. Primary 32Q45; Secondary 14J70, 14J29. Key words and phrases. Brody hyperbolicity, cyclic covers, hypersurfaces. The author was partially supported by NSF grant DMS-0968337.
Keywords
- Brody hyperbolicity
- Cyclic covers
- Hypersurfaces
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics