Algebraically hyperbolic manifolds have finite automorphism groups

Fedor A. Bogomolov; Ljudmila Kamenova; Misha Verbitsky

doi:10.1142/S0219199719500032

Algebraically hyperbolic manifolds have finite automorphism groups

Fedor A. Bogomolov
, Ljudmila Kamenova
, Misha Verbitsky

Mathematics

New York University
Higher School of Economics
Instituto National de Matemática Pura e Aplicada

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

2 Scopus citations

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
Article number	1950003
Journal	Communications in Contemporary Mathematics
Volume	22
Issue number	2
DOIs	https://doi.org/10.1142/S0219199719500032
State	Published - Mar 1 2020

Keywords

Albanese map
Algebraic hyperbolicity
Kobayashi hyperbolicity
group of automorphisms

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10.1142/S0219199719500032

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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.",

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AU - Verbitsky, Misha

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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 - Kobayashi hyperbolicity

KW - group of automorphisms

UR - https://www.scopus.com/pages/publications/85060781882

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Algebraically hyperbolic manifolds have finite automorphism groups

Abstract

Keywords

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