Coarse moduli space for polarized compact Kähler manifolds (Q1061279)

This paper shows the existence of a separated analytic coarse moduli space for the compact non-uniruled polarized Kähler manifolds (i.e. pairs (X,\(\omega)\) consisting of a compact manifold and the class \(\omega \in H^ 2(X,{\mathbb{R}})\) of a Kähler form on X, so that X cannot be covered by an analytic family of \({\mathbb{P}}_ 1({\mathbb{C}})'s)\). The method of proof is analogous to that of Narasimhan-Simha in the case of X with ample canonical class, and uses a Kählerian version of a theorem of Matsusaka-Mumford.