| Title:
|
A cohomological Steinness criterion for holomorphically spreadable complex spaces (English) |
| Author:
|
Vâjâitu, Viorel |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
655-667 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Stein space |
| Keyword:
|
1-convex space |
| Keyword:
|
branched Riemannian domain |
| Keyword:
|
holomorphically spreadable complex space |
| Keyword:
|
structurally acyclic space |
| MSC:
|
32C15 |
| MSC:
|
32C35 |
| MSC:
|
32E10 |
| MSC:
|
32L20 |
| idZBL:
|
Zbl 1224.32014 |
| idMR:
|
MR2672407 |
| . |
| Date available:
|
2010-07-20T17:07:10Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140596 |
| . |
| Reference:
|
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| Reference:
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