Algebraically hyperbolic manifolds have finite automorphism groups

Fedor A. Bogomolov, Ljudmila Kamenova, Misha Verbitsky

Research output: Contribution to journalArticlepeer-review

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)
Article number1950003
JournalCommunications in Contemporary Mathematics
Volume22
Issue number2
DOIs
StatePublished - 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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