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
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  • HAL Id : hal-01247045, version 2
  • ARXIV : 1512.06623

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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, In press, 51 (6). ⟨hal-01247045v2⟩

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