### 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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Article number | 1950003 |

Journal | Communications in Contemporary Mathematics |

Volume | 22 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2020 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Bogomolov, F. A., Kamenova, L., & Verbitsky, M. (2020). Algebraically hyperbolic manifolds have finite automorphism groups.

*Communications in Contemporary Mathematics*,*22*(2), [1950003]. https://doi.org/10.1142/S0219199719500032