Résumé
Dans cet article, nous étudions, sur des variétés Kähler compactes, les feuilletages holomorphes (éventuellement singuliers) dont le fibré conormal est pseudoeffectif. En utilisant la notion de courant à singularités minimales, nous montrons que l’on peut munir canoniquement l’espace des feuilles d’une métrique à courbure constante négative ou nulle dont les éventuelles dégénerescences sont localisées le long d’une hypersurface invariante “rigidement plongée” dans la variété.
Abstract
This paper deals with codimension one (may be singular) foliations on compact Kälher manifoldswhose conormal bundle is assumed to be pseudo-effective. Using currents with minimal singularities, we show that one can endow the space of leaves with a metric of constant non positive curvature wich may degenerate on a “rigidly” embedded invariant hypersurface.
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Touzet, F. Uniformisation de l’espace des feuilles de certains feuilletages de codimension un. Bull Braz Math Soc, New Series 44, 351–391 (2013). https://doi.org/10.1007/s00574-013-0017-7
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DOI: https://doi.org/10.1007/s00574-013-0017-7