Open sets which satisfy the Oka-Grauert principle in a Stein space

Abstract

Let X be a reduced Stein space of pure dimension n and let D be an open set of X . Assume that H k (D, O) = 0 for 2 ≤ k ≤ n − 1 and there exists a complex Lie group G of positive dimension such that the canonical map HWe prove that D is locally Stein at every point x ∈ ∂ D\Sing (X ). If X is normal, then we also prove that D has no boundary point removable along Sing (X ). If X is an orbifold, that is, if every x ∈ Sing (X ) is a quotient singular point, then D is locally Stein at every point x ∈ ∂ D.