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 complementary dimensions and with ample normal bundles have non-empty intersection. The third problem says that on a Fano manifold, the space of rational curves is a topological approximation to the space of all continuous maps. We describe possible approaches to these three problems.
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