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Compact Manifolds Covered by a Torus

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Abstract

Let X be a compact complex manifold which is the image of a complex torus by a holomorphic surjective map A→X. We prove that X is Kähler and that up to a finite étale cover, X is a product of projective spaces by a torus.

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Authors and Affiliations

  1. Institut Fourier, Université de Grenoble I, 38402, Saint-Martin-d’Hères, France

    Jean-Pierre Demailly

  2. KIAS, School of Mathematics, Seoul, Korea

    Jun-Muk Hwang

  3. Mathematisches Institut, Universität Bayreuth, Bayreuth, Germany

    Thomas Peternell

Authors
  1. Jean-Pierre Demailly
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  2. Jun-Muk Hwang
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  3. Thomas Peternell
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Corresponding author

Correspondence to Jean-Pierre Demailly.

Additional information

Dedicated to Gennadi Henkin.

J.-M. Hwang’s work was supported by the SRC Program of Korea Science and Engineering Foundation.

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Demailly, JP., Hwang, JM. & Peternell, T. Compact Manifolds Covered by a Torus. J Geom Anal 18, 324–340 (2008). https://doi.org/10.1007/s12220-008-9017-z

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  • DOI: https://doi.org/10.1007/s12220-008-9017-z

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