Holomorphic line bundles and Cartier divisors on domains in a Stein orbifold with disrete singularities

Abstract

Let X be a Stein orbifold of pure dimension n such that Sing(X) is discrete. Let D be an open set of X such that Hᵏ(D,O) = 0 for 2 ≤ k ≤ n - 1 and every topologically trivial holo-morphic line bundle on D is associated to some Cartier divisor on D.Then D is Stein