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Let be a complex space of dimension , not necessarily reduced, whose cohomology groups are of finite dimension (as complex vector spaces). We show that is Stein (resp., -convex) if, and only if, is holomorphically spreadable (resp., 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 -convexity.
Soit un groupe de Lie complexe et une forme réelle fermée de . Un couple est dit pseudo-convexe, s’il existe sur une fonction régulière, strictement p.s.h., invariante par l’action de et d’exhaustion sur . On dit que est à spectre imaginaire pur, si pour tout de Lie, les valeurs propres de ad sont imaginaires pures. Pour à radical simplement connexe, cette dernière propriété équivaut à la pseudo-convexité de . Pour pseudo-convexe et sous une hypothèse de sous-groupe discret,...
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