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A cohomological Steinness criterion for holomorphically spreadable complex spaces
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 655-667 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $X$ be a complex space of dimension $n$, not necessarily reduced, whose cohomology groups $H^1(X,{\cal O}), \ldots , H^{n-1}(X,{\cal O})$ 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). \endgraf 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.
Let $X$ be a complex space of dimension $n$, not necessarily reduced, whose cohomology groups $H^1(X,{\cal O}), \ldots , H^{n-1}(X,{\cal O})$ 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). \endgraf 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.
Classification : 32C15, 32C35, 32E10, 32L20
Keywords: Stein space; 1-convex space; branched Riemannian domain; holomorphically spreadable complex space; structurally acyclic space 
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Vâjâitu, Viorel. A cohomological Steinness criterion for holomorphically spreadable complex spaces. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 655-667. http://geodesic.mathdoc.fr/item/CMJ_2010_60_3_a4/

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