Quasi-projective quotients by compact equivalence relations
The author continues the construction of quasi-projective moduli schemes for certain moduli functors of polarized compact complex manifolds. Usually one considers the functor of polarized manifolds modulo \({\mathbb{Q}}\)-numerical equivalence [see e.g. \textit{H. Popp}, ``Moduli theory and classification theory of algebraic varieties'', Lect. Notes Math. 620 (1977; Zbl 0359.14005)]. In a previous paper [Invent. Math. 101, 521-543 (1990)], the author proved the existence of a coarse quasiprojective moduli scheme only for the functor of polarized manifolds modulo such isomorphisms which identify the polarizations. In the present article he proves the existence of a coarse quasi-projective moduli scheme for the usual moduli functor. Using results of a recent common paper with \textit{H. Esnault} [``Ample sheaves on moduli schemes'', algebraic geometry and analytic geometry, Proc. Conf., Tokyo/Japan 1990, 53-80 (1991)] he gives a description of an ample sheaf on this moduli scheme.
scientific article; zbMATH DE number 4204530