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Codimension one foliation with pseudo-effective conormal bundle - lecture 1

By Frédéric Touzet

Also appears in collection : Jean-Morlet Chair 2020 - Research School: Geometry and Dynamics of Foliations / Chaire Jean-Morlet 2020 - Ecole : Géométrie et dynamiques des feuilletages

Let X be a projective manifold equipped with a codimension 1 (maybe singular) distribution whose conormal sheaf is assumed to be pseudoeffective. Basic examples of such distributions are provided by the kernel of a holomorphic one form, necessarily closed when the ambient is projective. More generally, due to a theorem of Jean-Pierre Demailly, a distribution with conormal sheaf pseudoeffective is actually integrable and thus defines a codimension 1 holomorphic foliation F. In this series of lectures, we would aim at describing the structure of such a foliation, especially in the non abundant case, i.e when F cannot be defined by a holomorphic one form (even passing through a finite cover). 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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Citation data

  • DOI 10.24350/CIRM.V.19631003
  • Cite this video Touzet, Frédéric (05/05/2020). Codimension one foliation with pseudo-effective conormal bundle - lecture 1. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19631003
  • URL https://dx.doi.org/10.24350/CIRM.V.19631003

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