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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.
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.
@article{ASENS_2018__51_6_1457_0,
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://geodesic.mathdoc.fr/articles/10.24033/asens.2379/}
}
TY - JOUR AU - Claudon, Benoît AU - Loray, Frank AU - Pereira, Jorge Vitório AU - Touzet, Frédéric TI - Compact leaves of codimension one holomorphic foliations on projective manifolds JO - Annales scientifiques de l'École Normale Supérieure PY - 2018 SP - 1457 EP - 1506 VL - 51 IS - 6 PB - Société Mathématique de France. Tous droits réservés UR - http://geodesic.mathdoc.fr/articles/10.24033/asens.2379/ DO - 10.24033/asens.2379 LA - en ID - ASENS_2018__51_6_1457_0 ER -
%0 Journal Article %A Claudon, Benoît %A Loray, Frank %A Pereira, Jorge Vitório %A Touzet, Frédéric %T Compact leaves of codimension one holomorphic foliations on projective manifolds %J Annales scientifiques de l'École Normale Supérieure %D 2018 %P 1457-1506 %V 51 %N 6 %I Société Mathématique de France. Tous droits réservés %U http://geodesic.mathdoc.fr/articles/10.24033/asens.2379/ %R 10.24033/asens.2379 %G en %F ASENS_2018__51_6_1457_0
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://geodesic.mathdoc.fr/articles/10.24033/asens.2379/
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