Unbranched Riemann domains over Stein spaces and Cartier divisors

Abstract

It is proved that an unbranched Riemann domain $\Pi : X\rightarrow Y$ over an arbitrary Stein complex space of dimension $n\geq 2$ is Stein if and only if $X$ is cohomologically $2$-complete with respect to the structure sheaf ${\mathcal{O}}_{X}$ and every topologically trivial holomorphic line bundle over $X$ is associated to a Cartier divisor.