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

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
Externally published	Yes

Keywords

Brody hyperbolicity
Cyclic covers
Hypersurfaces

ASJC Scopus subject areas

Mathematics(all)
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.",

keywords = "Brody hyperbolicity, Cyclic covers, Hypersurfaces",

author = "Yuchen Liu",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

year = "2018",

doi = "10.1090/tran/7097",

language = "English (US)",

volume = "370",

pages = "5341--5357",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "8",

}

TY - JOUR

T1 - Hyperbolicity of cyclic covers and complements

AU - Liu, Yuchen

N1 - Funding Information: 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. Publisher Copyright: © 2018 American Mathematical Society.

PY - 2018

Y1 - 2018

N2 - 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.

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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DO - 10.1090/tran/7097

M3 - Article

AN - SCOPUS:85047128978

SN - 0002-9947

VL - 370

SP - 5341

EP - 5357

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 8

ER -

Hyperbolicity of cyclic covers and complements

Abstract

Keywords

ASJC Scopus subject areas

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