Compact complex manifolds whose complement of an analytic subset is Kahler

Abstract

In this paper, we consider a class of balanced manifolds and provide a proof of a problem proposed by Silva-that compact complex manifolds that are Kahler outside an analytic subset are balanced. Next, as a special case of this theorem, we prove that compact complex manifolds which are Kahler outside a Kahler submanifold are class C. Finally, we prove that a blow up along a submanifold of Hironaka's examples are Kahler, and we establish that Hironaka's examples are examples of this theorem.