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Steinness of bundles with fiber a Reinhardt bounded domain

Karl OeljeklausDan Zaffran — 2006

Bulletin de la Société Mathématique de France

Let E denote a holomorphic bundle with fiber D and with basis B . Both D and B are assumed to be Stein. For D a Reinhardt bounded domain of dimension d = 2 or 3 , we give a necessary and sufficient condition on D for the existence of a non-Stein such E (Theorem 1 ); for d = 2 , we give necessary and sufficient criteria for E to be Stein (Theorem 2 ). For D a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for E to be Stein (Theorem 3 ).

Two remarks on Kähler homogeneous manifolds

Bruce GilliganKarl Oeljeklaus — 2008

Annales de la faculté des sciences de Toulouse Mathématiques

We prove that every Kähler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger version of a question posed by Akhiezer for homogeneous spaces of nonsolvable algebraic groups in the case where the isotropy has the property that its intersection with the radical is Zariski dense in the radical.

Non-Kähler compact complex manifolds associated to number fields

Karl OeljeklausMatei Toma — 2005

Annales de l’institut Fourier

For algebraic number fields K with s > 0 real and 2 t > 0 complex embeddings and “admissible” subgroups U of the multiplicative group of integer units of K we construct and investigate certain ( s + t ) -dimensional compact complex manifolds X ( K , U ) . We show among other things that such manifolds are non-Kähler but admit locally conformally Kähler metrics when t = 1 . In particular we disprove a conjecture of I. Vaisman.

Vector fields and foliations on compact surfaces of class VII 0

Georges DlousskyKarl Oeljeklaus — 1999

Annales de l'institut Fourier

It is well-known that minimal compact complex surfaces with b 2 > 0 containing are in the class VII 0 of Kodaira. In fact, there are no other known examples. In this paper we prove that all surfaces with global spherical shells admit a singular holomorphic foliation. The existence of a numerically anticanonical divisor is a necessary condition for the existence of a global holomorphic vector field. Conversely, given the existence of a numerically anticanonical divisor, surfaces with a global vector field...

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