On the holomorphic separabilitiy of discrete quotients of complex Lie groups.
Homogeneous Complex Surfaces.
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 ).
Vector fields and foliations on compact surfaces of class
It is well-known that minimal compact complex surfaces with containing are in the class VII 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...
Compact complex threefolds of class L associated to polynomial automorphisms of C.
We construct new families of non-Kähler compact complex threefolds belonging to Kato's Class L. The construction uses certain polynomial automorphisms of C. We also study basic properties of our manifolds.
Two remarks on Kähler homogeneous manifolds
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
For algebraic number fields with real and complex embeddings and “admissible” subgroups of the multiplicative group of integer units of we construct and investigate certain -dimensional compact complex manifolds . We show among other things that such manifolds are non-Kähler but admit locally conformally Kähler metrics when . In particular we disprove a conjecture of I. Vaisman.
Une caractérisation des surfaces d'Inoue-Hirzebruch
On montre que parmi les surfaces compactes complexes de classe avec , les surfaces d’Inoue-Hirzebruch sont caractérisées par le fait qu’elles possèdent deux champs de vecteurs tordus. Ce résultat est un pas vers la compréhension des feuilletages sur les surfaces .
The Bergman kernel of the minimal ball and applications
In this note we compute the Bergman kernel of the unit ball with respect to the smallest norm in that extends the euclidean norm in and give some applications.
On proper R-actions on hyperbolic Stein surfaces.
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