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.
Citation
Viorel Vâjâitu. "Locally Stein domains over holomorphically convex manifolds." J. Math. Kyoto Univ. 48 (1) 133 - 148, 2008. https://doi.org/10.1215/kjm/1250280978
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