Abstract
Let X be a projective manifold equipped with a codimension 1 (maybe singular) distribution whose conormal sheaf is assumed to be pseudoeffective. By a theorem of Jean–Pierre Demailly, this distribution is actually integrable and thus defines a codimension 1 holomorphic foliation \( \mathcal{F} \). We aim at describing the structure of such a foliation, especially in the non-abundant case: It turns out that \( \mathcal{F} \) is the pull-back of one of the “canonical foliations” on a Hilbert modular variety. This result remains valid for “logarithmic foliated pairs.”
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Acknowledgements
It’s a pleasure to thank Dominique Cerveau, Frank Loray, and Jorge Vitório Pereira for valuable and helpful discussions. I also thank the referee for pointing out some mistakes and inaccuracies in the preliminary version.
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Touzet, F. (2016). On the Structure of Codimension 1 Foliations with Pseudoeffective Conormal Bundle. In: Cascini, P., McKernan, J., Pereira, J.V. (eds) Foliation Theory in Algebraic Geometry. Simons Symposia. Springer, Cham. https://doi.org/10.1007/978-3-319-24460-0_7
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DOI: https://doi.org/10.1007/978-3-319-24460-0_7
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