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Higher dimensional tautological inequalities and applications

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Abstract

We study the degeneracy of holomorphic mappings tangent to holomorphic foliations on projective manifolds. Using Ahlfors currents in higher dimension, we obtain several strong degeneracy statements such as the proof of a generalized Green-Griffiths–Lang conjecture for threefolds with holomorphic foliations of codimension one.

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Acknowledgments

We would like to thank Michael McQuillan for many interesting discussions on the subject of this paper. We also thank Serge Cantat, Dominique Cerveau, Charles Favre, Daniel Panazzolo and Frédéric Touzet for useful conversations.

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Authors and Affiliations

  1. Institut de Recherche Mathématique Avancée, Université de Strasbourg et CNRS, 7, rue René Descartes, 67084 , Strasbourg Cédex, France

    Carlo Gasbarri & Gianluca Pacienza

  2. Laboratoire d’Analyse, Topologie, Probabilités, Université d’Aix-Marseille et CNRS, 39, rue Frédéric Joliot-Curie, 13453 , Marseille Cedex 13, France

    Erwan Rousseau

Authors
  1. Carlo Gasbarri
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  2. Gianluca Pacienza
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  3. Erwan Rousseau
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Correspondence to Carlo Gasbarri.

Additional information

G. Pacienza is partially supported by the project CLASS (ANR-2010-JCJC-0111-01) of the Agence Nationale de la Recherche. E. Rousseau is partially supported by project COMPLEXE (ANR-08-JCJC-0130-01) of the Agence Nationale de la Recherche.

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Gasbarri, C., Pacienza, G. & Rousseau, E. Higher dimensional tautological inequalities and applications. Math. Ann. 356, 703–735 (2013). https://doi.org/10.1007/s00208-012-0857-2

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  • DOI: https://doi.org/10.1007/s00208-012-0857-2

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