Unbranched Riemann domains over Stein spaces

Details Unbranched Riemann domains over Stein spaces Unbranched Riemann domains over Stein spaces

2009-11-10

arxiv.org/abs/0911.1800v2

Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 7, Number 1 (2011), pp. 77-81

Mathematics

Complex Variables

6 pages, no figures

Scientific paper

In this article, we show that if $\Pi: X\rightarrow \Omega$ is an unbranched
Riemann domain with $\Omega$ Stein and $\Pi$ a locally 1-complete morphism,
then $X$ is Stein. This gives in particular a positive answer to the local
Steiness problem, namely if $X$ is a Stein space and, if $\Omega$ is a locally
Stein open set in $X$, then $\Omega$ is Stein.

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