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Algebraic integrability of foliations with numerically trivial canonical bundle

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Abstract

Given a reflexive sheaf on a mildly singular projective variety, we prove a flatness criterion under certain stability conditions. This implies the algebraicity of leaves for sufficiently stable foliations with numerically trivial canonical bundle such that the second Chern class does not vanish. Combined with the recent works of Druel and Greb–Guenancia–Kebekus this establishes the Beauville–Bogomolov decomposition for minimal models with trivial canonical class.

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Acknowledgements

We thank S. Cantat and P. Graf for some very useful references. This work was partially supported by the Agence Nationale de la Recherche grant project Foliage (ANR-16-CE40-0008) and by the DFG project “Zur Positivität in der komplexen Geometrie”. We thank the referees for numerous suggestions to improve this text.

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  1. CNRS, LJAD, Université Côte d’Azur, Nice, France

    Andreas Höring

  2. Mathematisches Institut, Universität Bayreuth, 95440, Bayreuth, Germany

    Thomas Peternell

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Höring, A., Peternell, T. Algebraic integrability of foliations with numerically trivial canonical bundle. Invent. math. 216, 395–419 (2019). https://doi.org/10.1007/s00222-018-00853-2

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