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Foliations with vanishing Chern classes

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To the memory of Marco Brunella.

Abstract

In this paper we aim at the description of foliations having tangent sheaf T F with c 1 (T F) = c 2(T F) = 0 on non-uniruled projective manifolds. We prove that the universal covering of the ambient manifold splits as a product, and that the Zariski closure of a general leaf of F is an Abelian variety. It turns out that the analytic type of the Zariski closures of leaves may vary from leaf to leaf. We discuss how this variation is related to arithmetic properties of the tangent sheaf of the foliation.

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Authors and Affiliations

  1. IMPA, Estrada Dona Castorina, 110, Horto, Rio de Janeiro, Brazil

    Jorge Vitório Pereira

  2. IRMAR, Campus de Beaulieu, 35042, Rennes Cedex, France

    Frédéric Touzet

Authors
  1. Jorge Vitório Pereira
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  2. Frédéric Touzet
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Correspondence to Jorge Vitório Pereira.

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Pereira, J.V., Touzet, F. Foliations with vanishing Chern classes. Bull Braz Math Soc, New Series 44, 731–754 (2013). https://doi.org/10.1007/s00574-013-0032-8

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  • DOI: https://doi.org/10.1007/s00574-013-0032-8

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