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A cohomological Steinness criterion for holomorphically spreadable complex spaces

Viorel Vâjâitu (2010)

Czechoslovak Mathematical Journal

Let X be a complex space of dimension n , not necessarily reduced, whose cohomology groups H 1 ( X , 𝒪 ) , ... , H n - 1 ( X , 𝒪 ) are of finite dimension (as complex vector spaces). We show that X is Stein (resp., 1 -convex) if, and only if, X is holomorphically spreadable (resp., X is holomorphically spreadable at infinity). This, on the one hand, generalizes a known characterization of Stein spaces due to Siu, Laufer, and Simha and, on the other hand, it provides a new criterion for 1 -convexity.

Action d'une forme réelle d'un groupe de Lie complexe sur les fonctions plurisousharmoniques

Jean-Jacques Loeb (1985)

Annales de l'institut Fourier

Soit G C un groupe de Lie complexe et G R une forme réelle fermée de G C . Un couple ( G C , G R ) est dit pseudo-convexe, s’il existe sur G C une fonction régulière, strictement p.s.h., invariante par l’action de G R et d’exhaustion sur G C / G R . On dit que G R est à spectre imaginaire pur, si pour tout X de Lie ( G R ) , les valeurs propres de ad X sont imaginaires pures. Pour G C à radical simplement connexe, cette dernière propriété équivaut à la pseudo-convexité de ( G C , G R ) . Pour ( G C , G R ) pseudo-convexe et sous une hypothèse de sous-groupe discret,...

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