Our project focuses on three problems on Kahler manifolds. The first problem deals with the deformation of Kahler manifolds. Given an analytic family of compact complex manifolds, we want to prove that the non-Kahler locus is a countable union of analytic subsets of the base. The second problem is the well-known conjecture of Hartshorne. It states that in a Kahler manifold, two subvarieties of com ...