On the structure of codimension 1 foliations with pseudoeffective conormal bundle. - Archive ouverte HAL Access content directly
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On the structure of codimension 1 foliations with pseudoeffective conormal bundle.

Abstract

Let $X$ 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 $\F$. We aim at describing the structure of such a foliation, especially in the non abundant case: It turns out that $\F$ 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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Dates and versions

hal-00984243 , version 1 (28-04-2014)

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Cite

Frédéric Touzet. On the structure of codimension 1 foliations with pseudoeffective conormal bundle.. Paolo Cascini; James McKernan; Jorge Vitorio Pereira. Foliation theory in algebraic geometry, Springer, pp.157-216, 2016, Simons Symposia, 978-3-319-24458-7. ⟨10.1007/978-3-319-24460-0⟩. ⟨hal-00984243⟩
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