Hyperbolicity of cyclic covers and complements

Yuchen Liu

doi:10.1090/tran/7097

Hyperbolicity of cyclic covers and complements

Yuchen Liu^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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)
Pages (from-to)	5341-5357
Number of pages	17
Journal	Transactions of the American Mathematical Society
Volume	370
Issue number	8
DOIs	https://doi.org/10.1090/tran/7097
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

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10.1090/tran/7097

Cite this

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title = "Hyperbolicity of cyclic covers and complements",

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.",

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AB - 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.

KW - Brody hyperbolicity

KW - Cyclic covers

KW - Hypersurfaces

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Hyperbolicity of cyclic covers and complements

Abstract

Funding

Keywords

ASJC Scopus subject areas

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