Unbranched Riemann domains over Stein spaces and Cartier divisors

Abstract

It is proved that an unbranched Riemann domain $\Pi :X\to Y$ over an arbitrary Stein complex space of dimension $n\ge 2$ 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.

8 pages