Compact leaves of codimension one  holomorphic foliations  on projective manifolds

Claudon, Benoît; Loray, Frank; Pereira, Jorge Vitório; Touzet, Frédéric

doi:10.24033/asens.2379

Compact leaves of codimension one holomorphic foliations on projective manifolds
[Feuilles compactes des feuilletages holomorphes de codimension 1 sur les variétés projectives]

Claudon, Benoît ; Loray, Frank ; Pereira, Jorge Vitório ; Touzet, Frédéric

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 51 (2018) no. 6, pp. 1457-1506.

Résumé
Abstract

Cet article étudie les feuilletages de codimension 1 sur les variétés projectives admettant une feuille compacte (ne rencontrant pas le lieu singulier du feuilletage). Les interactions entre la théorie de Ueda (ordre de platitude du fibré normal de la feuille) et la représentation d'holonomie (dynamique du feuilletage dans la direction transverse) sont explorées. Nous envisageons en particulier les problématiques suivantes : existence de feuilletages admettant pour feuille une hypersurface donnée possédant un fibré normal topologiquement de torsion, étude de la structure globale des feuilletages ayant une feuille compacte d'holonomie abélienne (resp. résoluble) et résultats de factorisations.

This article studies codimension one foliations on projective manifolds having a compact leaf (free of singularities). It explores the interplay between Ueda theory (order of flatness of the normal bundle) and the holonomy 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.

MR Zbl

DOI : 10.24033/asens.2379

Classification : 37F75, 14J70, 14B20.
Keywords: Codimension one holomorphic foliations, compact leaves, holonomy representations, Ueda theory, transversely affine foliations.
Mot clés : Feuilletages holomorphes de codimension 1, feuilles compactes, représentations d'holonomie, théorie de Ueda, feuilletages transversalement affines.

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     author = {Claudon, Beno{\^\i}t and Loray, Frank and Pereira, Jorge Vit\'orio and Touzet, Fr\'ed\'eric},
     title = {Compact leaves of codimension one  holomorphic foliations  on projective manifolds},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {1457--1506},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 51},
     number = {6},
     year = {2018},
     doi = {10.24033/asens.2379},
     mrnumber = {3940902},
     zbl = {1454.37049},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.2379/}
}

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Claudon, Benoît; Loray, Frank; Pereira, Jorge Vitório; Touzet, Frédéric. Compact leaves of codimension one  holomorphic foliations  on projective manifolds. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 51 (2018) no. 6, pp. 1457-1506. doi : 10.24033/asens.2379. http://www.numdam.org/articles/10.24033/asens.2379/

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