### Abstract

A projective manifold M is algebraically hyperbolic if there exists a positive constant A such that the degree of any curve of genus g on M is bounded from above by A(g - 1). A classical result is that Kobayashi hyperbolicity implies algebraic hyperbolicity. It is known that Kobayashi hyperbolic manifolds have finite automorphism groups. Here, we prove that, more generally, algebraically hyperbolic projective manifolds have finite automorphism groups.

Original language | English (US) |
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Journal | Communications in Contemporary Mathematics |

DOIs | |

State | Published - Jan 1 2019 |

### Fingerprint

### Keywords

- Albanese map
- Algebraic hyperbolicity
- group of automorphisms
- Kobayashi hyperbolicity

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications in Contemporary Mathematics*. https://doi.org/10.1142/S0219199719500032

**Algebraically hyperbolic manifolds have finite automorphism groups.** / Bogomolov, Fedor; Kamenova, Ljudmila; Verbitsky, Misha.

Research output: Contribution to journal › Article

*Communications in Contemporary Mathematics*. https://doi.org/10.1142/S0219199719500032

}

TY - JOUR

T1 - Algebraically hyperbolic manifolds have finite automorphism groups

AU - Bogomolov, Fedor

AU - Kamenova, Ljudmila

AU - Verbitsky, Misha

PY - 2019/1/1

Y1 - 2019/1/1

N2 - A projective manifold M is algebraically hyperbolic if there exists a positive constant A such that the degree of any curve of genus g on M is bounded from above by A(g - 1). A classical result is that Kobayashi hyperbolicity implies algebraic hyperbolicity. It is known that Kobayashi hyperbolic manifolds have finite automorphism groups. Here, we prove that, more generally, algebraically hyperbolic projective manifolds have finite automorphism groups.

AB - A projective manifold M is algebraically hyperbolic if there exists a positive constant A such that the degree of any curve of genus g on M is bounded from above by A(g - 1). A classical result is that Kobayashi hyperbolicity implies algebraic hyperbolicity. It is known that Kobayashi hyperbolic manifolds have finite automorphism groups. Here, we prove that, more generally, algebraically hyperbolic projective manifolds have finite automorphism groups.

KW - Albanese map

KW - Algebraic hyperbolicity

KW - group of automorphisms

KW - Kobayashi hyperbolicity

UR - http://www.scopus.com/inward/record.url?scp=85060781882&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85060781882&partnerID=8YFLogxK

U2 - 10.1142/S0219199719500032

DO - 10.1142/S0219199719500032

M3 - Article

AN - SCOPUS:85060781882

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

SN - 0219-1997

ER -