Abstract
Let X be a complex space of dimension n, not necessarily reduced, whose cohomology groups H 1(X, \( \mathcal{O} \)), ...,H n−1(X, \( \mathcal{O} \)) 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.
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Vâjâitu, V. A cohomological steinness criterion for holomorphically spreadable complex spaces. Czech Math J 60, 655–667 (2010). https://doi.org/10.1007/s10587-010-0060-0
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DOI: https://doi.org/10.1007/s10587-010-0060-0
Keywords
- Stein space
- 1-convex space
- branched Riemannian domain
- holomorphically spreadable complex space
- structurally acyclic space