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Finiteness Theorems and Hyperbolic Manifolds

  • A. N. Parshin
Chapter
Part of the Modern Birkhäuser Classics book series (volume 88)

Abstract

Let f : XS be a proper smooth holomorphic family of projective algebraic varieties. If we fix a base point s0S, then we have monodromy action of the fundamental group
$$\rho :{\pi _1}\left( {{S_1}{s_0}} \right) \to Aut{\kern 1pt} {H^p}\left( {{X_0}Z} \right)$$
where X0 is a fiber over s0. The following results were proved using a hyperbolic metric which was introduced by S. Kobayashi [10], [11].

Keywords

Exact Sequence Conjugacy Class Fundamental Group Complex Manifold Abelian Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2007

Authors and Affiliations

  • A. N. Parshin
    • 1
  1. 1.Steklov Mathematical InstituteAcademy of Sciences of USSRMoscow GSP-1USSR

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