A cohomological Steinness criterion for holomorphically spreadable complex spaces

Viorel Vâjâitu

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 3, page 655-667
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Vâjâitu, Viorel. "A cohomological Steinness criterion for holomorphically spreadable complex spaces." Czechoslovak Mathematical Journal 60.3 (2010): 655-667. <http://eudml.org/doc/38033>.

@article{Vâjâitu2010,
abstract = {Let $X$ be a complex space of dimension $n$, not necessarily reduced, whose cohomology groups $H^1(X,\{\mathcal \{O\}\}), \ldots , H^\{n-1\}(X,\{\mathcal \{O\}\})$ 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.},
author = {Vâjâitu, Viorel},
journal = {Czechoslovak Mathematical Journal},
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},
language = {eng},
number = {3},
pages = {655-667},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A cohomological Steinness criterion for holomorphically spreadable complex spaces},
url = {http://eudml.org/doc/38033},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Vâjâitu, Viorel
TI - A cohomological Steinness criterion for holomorphically spreadable complex spaces
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 3
SP - 655
EP - 667
AB - Let $X$ be a complex space of dimension $n$, not necessarily reduced, whose cohomology groups $H^1(X,{\mathcal {O}}), \ldots , H^{n-1}(X,{\mathcal {O}})$ 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/38033
ER -

References

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