Franc Forstnerič - Non singular holomorphic foliations on Stein manifolds (Part 1)

Auteur(s) : FORSTNERIČ FRANC    19-06-2012  Éditeur(s) : Fanny Bastien;     Description : A nonsingular holomorphic foliation of codimension on a complex manifold is locally given by the level sets of a holomorphic submersion to the Euclidean space . If is a Stein manifold, there also exist plenty of global foliations of this form, so long as there are no topological obstructions. More precisely, if then any -tuple of pointwise linearly independent (1,0)-forms can be continuously deformed to a -tuple of differentials where is a holomorphic submersion of to . Such a submersion always exists if is no more than the integer part of . More generally, if is a complex vector subbundle of the tangent bundle such that is a flat bundle, then is homotopic (through complex vector subbundles of ) to an integrable subbundle, i.e., to the tangent bundle of a nonsingular holomorphic foliation on . I will prove these results and discuss open problems, the most interesting one of them being related to a conjecture of Bogomolov. Mots-clés libres : Mathèmatiques, Grenoble, école d'été, courbes, institut fourier, summer school, feuilletages, holomorphic foliations Classification générale : Mathématiques Accès à la ressource : http://www.canal-u.tv/video/institut_fourier/franc... rtmpt://fms2.cerimes.fr:80/vod/institut_fourier/fr... Conditions d'utilisation : Droits réservés à l'éditeur et aux auteurs. CC BY-NC-ND 4.0

DONNEES PEDAGOGIQUES Type pédagogique : cours / présentation Niveau : doctorat DONNEES TECHNIQUES Format : video/x-flv Taille : 3.31 Go Durée d'exécution : 1 heure 31 minutes 20 secondes

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