Decomposition of Compact Complex Varieties and the Cancellation Problem.
We study compact Kähler manifolds admitting nonvanishing holomorphic vector fields, extending the classical birational classification of projective varieties with tangent vector fields to a classification modulo deformation in the Kähler case, and biholomorphic in the projective case. We introduce and analyze a new class of , and show that they form a smooth subspace in the Kuranishi space of deformations of the complex structure of . We extend Calabi’s theorem on the structure of compact Kähler...
In this paper we study the degeneration of both the cohomology and the cohomotopy Frölicher spectral sequences in a special class of complex manifolds, namely the class of compact nilmanifolds endowed with a nilpotent complex structure. Whereas the cohomotopy spectral sequence is always degenerate for such a manifold, there exist many nilpotent complex structures on compact nilmanifolds for which the classical Frölicher spectral sequence does not collapse even at the second term.
On démontre que les domaines bornés, pseudo-convexes, à frontière lisse, de type fini dans , ayant un groupe d’automorphismes non compact sont biholomorphes à des domaines de la forme , où est un polynôme sousharmonique dont le degré est majoré par le type de la frontière du domaine.