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Seminários do IMPA

Geometria Diferencial

Título |
Algebraically hyperbolic manifolds have finite automorphism groups |

Expositor |
Misha Verbitsky
IMPA |

Data |
Terça-feira, 8 de maio de 2018, 15:30 |

Local |
Sala 236. |

Resumo |

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). Kobayashi hyperbolic manifolds are compact manifolds contaning no entire curves (holomorphic images of C). Examples of hyperbolic manifolds include all Kahler manifolds with negative holomorphic sectional curvature. Kobayashi hyperbolic manifolds are equipped with a natural Finsler metric called Kobayashi metric, invariant under complex automorphisms. This can be used to show that the automorphism group of Kobayashi hyperbolic manifolds is finite. It is not hard to see that Kobayashi hyperbolicity implies algebraic hyperbolicity for projective manifolds. Conjecturally, algebraic hyperbolicity is equivalent to Kobayashi hyperbolicity. I will prove that algebraically hyperbolic manifolds have finite automorphism groups. This is a joint work with Fedor Bogomolov and Ljudmila Kamenova.