Mihnea Colţoiu

Some open problems concerning q-convexity and Stein spaces

ABSTRACT We discuss some open problems in the theory of analytic pseudoconvexity. We focus our attention especially on q-complete spaces and Stein spaces.

The Levi problem in the blow-up

We prove that a locally Stein open subset of the blow-up of Cn at a point is Stein if and only if it does not contain a subset of the form U n A where A is the exceptional divisor andU is an open neighborhood of A. We also study an analogous statement for locally Stein open subsets of line bundles ove r Pn.