The local Steiness problem with singularities
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2009
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911375162343424 |
|---|---|
| author | Alaoui, Youssef |
| author_facet | Alaoui, Youssef |
| contents | In this article, we prove that if $Π: X\rightarrow Ω$ is an unbranched Riemann domain with $Ω$ Stein of dimension $n$ and $Π$ a locally $q$-complete morphism, then $X$ is cohomologically $q$-complete if $n\geq 3$ and $1\leq q\leq n-2$ or if $Ω$ has dimension $2$ and $1\leq q\leq 2$. This generalizes a well-known result which is obtained in ~\cite{ref3} for $q=1$ when $X$ and $Ω$ have isolated singularities and, gives in particular a positive answer to the local Steiness problem, namely if $X$ is a Stein space and $Ω$ a locally Stein open subset of $X$, then $Ω$ is Stein. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0911_1800 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | The local Steiness problem with singularities Alaoui, Youssef Complex Variables 32E10, 32E40 In this article, we prove that if $Π: X\rightarrow Ω$ is an unbranched Riemann domain with $Ω$ Stein of dimension $n$ and $Π$ a locally $q$-complete morphism, then $X$ is cohomologically $q$-complete if $n\geq 3$ and $1\leq q\leq n-2$ or if $Ω$ has dimension $2$ and $1\leq q\leq 2$. This generalizes a well-known result which is obtained in ~\cite{ref3} for $q=1$ when $X$ and $Ω$ have isolated singularities and, gives in particular a positive answer to the local Steiness problem, namely if $X$ is a Stein space and $Ω$ a locally Stein open subset of $X$, then $Ω$ is Stein. |
| title | The local Steiness problem with singularities |
| topic | Complex Variables 32E10, 32E40 |
| url | https://arxiv.org/abs/0911.1800 |