Algebraically hyperbolic manifolds have finite automorphism groups

Fedor Bogomolov, Ljudmila Kamenova, Misha Verbitsky

Research output: Contribution to journalArticle

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 languageEnglish (US)
JournalCommunications in Contemporary Mathematics
DOIs
StatePublished - Jan 1 2019

Fingerprint

Hyperbolic Manifold
Hyperbolicity
Automorphism Group
Finite Group
Genus
Imply
Curve

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Communications in Contemporary Mathematics, 01.01.2019.

Research output: Contribution to journalArticle

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