On Strongly Pseudo-convex Kähler Manifolds.
In this paper we show that a 1-convex (i.e., strongly pseudoconvex) manifold , with 1- dimensional exceptional set and finitely generated second homology group , is embeddable in if and only if is Kähler, and this case occurs only when does not contain any effective curve which is a boundary.
In this paper, we show that if and are algebraic real hypersurfaces in (possibly different) complex spaces of dimension at least two and if is a holomorphic mapping defined near a neighborhood of so that , then is also algebraic. Our proof is based on a careful analysis on the invariant varieties and reduces to the consideration of many cases. After a slight modification, the argument is also used to prove a reflection principle, which allows our main result to be stated for mappings...
Soit une variété -analytique quasi-homogène sous l’action d’un groupe de Lie complexe commutatif. On démontre que admet une modification lisse kählérienne si et seulement si ; on en déduit aussi un critère d’algébricité.