-
- Date de réalisation : 22 Juin 2012
- Durée du programme : 97 min
- Classification Dewey : Mathématiques
-
- Catégorie : Cours magistraux
- Niveau : niveau Doctorat (LMD), Recherche
- Disciplines : Géométrie
- Collections : Ecoles d'été, 2012
- ficheLom : Voir la fiche LOM
-
- Réalisateur(s) : Bastien Fanny
-
- Langue : Anglais
- Mots-clés : Grenoble, école d'été, mathématiques , institut fourier, summer school, holomorphic foliations
- Conditions d’utilisation / Copyright : CC BY-NC-ND 4.0
Dans la même collection
























Franc Forstnerič - Non singular holomorphic foliations on Stein manifolds (Part 4)
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.
commentaires
Ajouter un commentaire Lire les commentaires