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Keywords:
Stein space; 1-convex space; branched Riemannian domain; holomorphically spreadable complex space; structurally acyclic space
Stein space; 1-convex space; branched Riemannian domain; holomorphically spreadable complex space; structurally acyclic space
Summary:
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.
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