Quasi-projective quotients by compact equivalence relations
type: Item
instance of: scholarly article
title: Quasi-projective quotients by compact equivalence relations
zbMATH Open document ID: 0729.14010
DOI: 10.1007/BF01446573
author: Eckart Viehweg
published in: Mathematische Annalen
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164782
review text: 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.
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14D22
Mathematics Subject Classification ID: 14J10
zbMATH DE Number: 4204530
zbMATH Keywords: nef
zbMATH Keywords: canonical bundle
zbMATH Keywords: coarse quasiprojective moduli scheme
zbMATH Keywords: polarizations
reviewed by: Bernd Kreußler
MaRDI profile type: Publication
cites work: Versal deformations and algebraic stacks
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description: scientific article; zbMATH DE number 4204530