## Journal of Mathematics of Kyoto University

### Locally Stein domains over holomorphically convex manifolds

Viorel Vâjâitu

#### Abstract

Let $\pi : Y \longrightarrow X$ be a domain over a complex space $X$. Assume that $\pi$ is locally Stein. Then we show that $Y$ is Stein provided that $X$ is Stein and either there is an open set $W$ containing $X_{\mathrm{sing}}$ with $\pi^{-1}(W)$ Stein or $\pi$ is locally hyperconvex over any point in $X_{\mathrm{sing}}$. In the same vein we show that, if $X$ is $q$-complete and $X$ has isolated singularities, then $Y$ results $q$-complete.

#### Article information

Source
J. Math. Kyoto Univ., Volume 48, Number 1 (2008), 133-148.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250280978

Digital Object Identifier
doi:10.1215/kjm/1250280978

Mathematical Reviews number (MathSciNet)
MR2437894

Zentralblatt MATH identifier
1158.32004

#### Citation

Vâjâitu, Viorel. Locally Stein domains over holomorphically convex manifolds. J. Math. Kyoto Univ. 48 (2008), no. 1, 133--148. doi:10.1215/kjm/1250280978. https://projecteuclid.org/euclid.kjm/1250280978