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
Publication statusPublished - Jan 1 2019

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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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