Finiteness Theorems and Hyperbolic Manifolds

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


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].


Exact Sequence Conjugacy Class Fundamental Group Complex Manifold Abelian Variety 
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© 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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