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Finiteness Theorems and Hyperbolic Manifolds

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The Grothendieck Festschrift

Part of the book series: Modern Birkhäuser Classics ((MBC,volume 88))

Abstract

Let f : X → S be a proper smooth holomorphic family of projective algebraic varieties. If we fix a base point s0 ∈ S, 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 X 0 is a fiber over s 0. The following results were proved using a hyperbolic metric which was introduced by S. Kobayashi [10], [11].

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Authors and Affiliations

  1. Steklov Mathematical Institute, Academy of Sciences of USSR, Ul. Vavilova 42, 117966, Moscow GSP-1, USSR

    A. N. Parshin

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  1. A. N. Parshin
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Editor information

Editors and Affiliations

  1. Institut des Hautes Études Scientifiques, F-91440, Bures-sur-Yvette, France

    Pierre Cartier

  2. Département de Mathématiques, Université de Paris-Sud, F-91405, Orsay, France

    Luc Illusie  & Gérard Laumon  & 

  3. Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA

    Nicholas M. Katz

  4. Max-Planck Institut für Mathematik, D-53111, Bonn, Germany

    Yuri I. Manin

  5. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Kenneth A. Ribet

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Dedicated to A. Grothendieck

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Parshin, A.N. (2007). Finiteness Theorems and Hyperbolic Manifolds. In: Cartier, P., Illusie, L., Katz, N.M., Laumon, G., Manin, Y.I., Ribet, K.A. (eds) The Grothendieck Festschrift. Modern Birkhäuser Classics, vol 88. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4576-2_6

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  • DOI: https://doi.org/10.1007/978-0-8176-4576-2_6

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  • Print ISBN: 978-0-8176-4568-7

  • Online ISBN: 978-0-8176-4576-2

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