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Compact leaves of codimension one holomorphic foliations on projective manifolds

Abstract : This article studies codimension one foliations on projective man-ifolds having a compact leaf (free of singularities). It explores the interplay between Ueda theory (order of flatness of the normal bundle) and the holo-nomy representation (dynamics of the foliation in the transverse direction). We address in particular the following problems: existence of foliation having as a leaf a given hypersurface with topologically torsion normal bundle, global structure of foliations having a compact leaf whose holonomy is abelian (resp. solvable), and factorization results.
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Submitted on : Wednesday, August 29, 2018 - 9:30:20 AM
Last modification on : Friday, July 10, 2020 - 4:17:59 PM
Long-term archiving on: : Friday, November 30, 2018 - 12:53:54 PM

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Benoît Claudon, Frank Loray, Jorge Pereira, Frédéric Touzet. Compact leaves of codimension one holomorphic foliations on projective manifolds. Annales Scientifiques de l'École Normale Supérieure, Elsevier Masson, 2018, 51 (6), pp.1457-1506. ⟨10.24033/asens.2379⟩. ⟨hal-01247045v2⟩

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