A COHOMOLOGICAL STEINNESS CRITERION FOR HOLOMORPHICALLY SPREADABLE COMPLEX SPACES

作者：Vajaitu Viorel^*

来源：Czechoslovak Mathematical Journal, 2010, 60(3): 655-667.

• Stein space
• 1-convex space
• branched Riemannian domain
• holomorphically spreadable complex space
• structurally acyclic space

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.

• 出版日期2010-9