Unbranched Riemann domains over Stein spaces and Cartier divisors

2008/10/04 by Youssef Alaoui, Alaoui, Youssef
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0810.0782

Abstract

It is proved that an unbranched Riemann domain Π: X→ Y over an arbitrary Stein complex space of dimension n≥ 2 is Stein if and only if X is cohomologically 2-complete with respect to the structure sheaf O_X and every topologically trivial holomorphic line bundle over X is associated to a Cartier divisor.

Related

• Notions of Stein spaces in non-archimedean geometry
• The local Steiness problem with singularities
• Holomorphic fiber bundle with Stein base and Stein fibers
• The L²-cohomology of a bounded smooth Stein Domain is not necessarily Hausdorff
• Steinness of bundles with fiber a Reinhardt bounded domain