Unbranched Riemann domains over Stein spaces and Cartier divisors

TL;DR

This paper establishes conditions under which unbranched Riemann domains over Stein spaces are themselves Stein, linking cohomological completeness and line bundle properties to the Stein condition.

Contribution

It proves that such Riemann domains are Stein if and only if they are cohomologically 2-complete and all topologically trivial line bundles are Cartier divisors.

Findings

Unbranched Riemann domains over Stein spaces are Stein under specified conditions.

Cohomological 2-completeness is equivalent to the Stein property in this context.

Topologically trivial line bundles correspond to Cartier divisors on these domains.

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.