Special neighborhoods of subsets in complex spaces.
Spherical Stein manifolds and the Weyl involution
We consider an action of a connected compact Lie group on a Stein manifold by holomorphic transformations. We prove that the manifold is spherical if and only if there exists an antiholomorphic involution preserving each orbit. Moreover, for a spherical Stein manifold, we construct an antiholomorphic involution, which is equivariant with respect to the Weyl involution of the acting group, and show that this involution stabilizes each orbit. The construction uses some properties of spherical subgroups...
Stein manifolds with compact symmetric center.
Stein Neighborhoods for Finite Preimages of Regular Domain.
Stein open subsets with analytic complements in compact complex spaces
Let Y be an open subset of a reduced compact complex space X such that X - Y is the support of an effective divisor D. If X is a surface and D is an effective Weil divisor, we give sufficient conditions so that Y is Stein. If X is of pure dimension d ≥ 1 and X - Y is the support of an effective Cartier divisor D, we show that Y is Stein if Y contains no compact curves, for all i > 0, and for every point x₀ ∈ X-Y there is an n ∈ ℕ such that is empty or has dimension 0, where is the map from...
Stein Quotients of Connected Complex Lie Groups.
Stein surfaces associated to intermediate Kato surfaces. (Surfaces de Stein associées aux surfaces de Kato intermédiaires.)
Steinness of bundles with fiber a Reinhardt bounded domain
Let denote a holomorphic bundle with fiber and with basis . Both and are assumed to be Stein. For a Reinhardt bounded domain of dimension or , we give a necessary and sufficient condition on for the existence of a non-Stein such (Theorem ); for , we give necessary and sufficient criteria for to be Stein (Theorem ). For a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for to be Stein (Theorem ).
Strange complex structures on Euclidean space.
Structure of leaves and the complex Kupka-Smale property
We study topology of leaves of -dimensional singular holomorphic foliations of Stein manifolds. We prove that for a generic foliation all leaves, except for at most countably many, are contractible, the rest are topological cylinders. We show that a generic foliation is complex Kupka-Smale.
Sur le problème de Lévi dans certains fibres.
Sur les espaces de Stein quasi-compacts en géométrie rigide
On étudie les espaces de Stein quasi-compacts (i.e. vérifiant pour tout et tout faisceau cohérent sur ). On établit un critère simple pour qu’un espace soit de Stein et on en déduit quelques conséquences.
Sur les quotients discrets de semi-groupes complexes
Soit un espace symétrique hermitien irréducible de type non-compact et soit le semi-groupe associé formé des compressions de . Soit un sous-groupe discret. Nous donnons une condition suffisante pour que le quotient soit une variété de Stein. En outre nous démontrons qu’en général n’est pas de Stein ce qui réfute une conjecture de Achab, Betten et Krötz.
Sur les relations d'équivalence ouvertes dans les espaces analytiques
Sur les voisinages tubulaires en Géométrie Analytique.
Survey of Oka theory.
The cohomology of an open subspace of a Stein spaces.
The Hartogs-type extension theorem for meromorphic maps intor compact Kähler manifolds.
The Levi problem in Stein spaces.
The Levi Problem on Complex Spaces with Singularities.