Moduli of polarized Kähler manifolds (Q1075468)

The two main results of the paper are: Theorem 1. Let K be a collection of compact polarized Kähler manifolds. Then there exists a coarse moduli space for K, if (i) K is stable under small Kähler deformations, (ii) given Kähler families \((X\to S,\lambda_{X/S})\) and \((Y\to S,\lambda_{Y/S})\) then the holomorphic mapping \(Isom_ S^{\lambda}(X,Y)\to S\) is proper. Theorem 2. There exists the coarse moduli space for the class K of all non-ruled, polarized manifolds, whose small deformations still have this property. As stated by the author: ''It was brought to the author's attention that A. Fujiki proved essentially the same result in a forthcoming paper.''