Uniformisation de l'espace des feuilles de certains feuilletages de codimension 1.

Frédéric Touzet (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

This paper deals with codimension one (may be singular) foliations on compact Kälher manifolds whose 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.

Mots clés: feuilletage; classe pseudo-effective; holomorphic foliations

Domaines: Variables complexes [math.CV]

Frédéric Touzet. Uniformisation de l'espace des feuilles de certains feuilletages de codimension 1.. Boletim da Sociedade Brasileira de Matemática / Bulletin of the Brazilian Mathematical Society, 2013, 44 (3), pp.351-391. ⟨10.1007/s00574-013-0017-7⟩. ⟨hal-00579387⟩