On the embedding of 1-convex manifolds with 1-dimensional exceptional set

In this paper we prove two main results. Theorem I: Let X be a 1-convex manifold with 1-dimensional exceptional set S. Then X is Kähler if and only if S does not contain any effective curve which is a boundary. Theorem II: Let X be a 1-convex manifold with 1-dimensional exceptional set S. If H2(X,Z) is finitely generated, then X is embeddable if and only if it is Kähler