Kähler spaces and proper open morphisms
type: Item
instance of: scholarly article
title: Kähler spaces and proper open morphisms
zbMATH Open document ID: 0632.53059
DOI: 10.1007/BF01457500
author: Jean Varouchas
published in: Mathematische Annalen
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164492
review text: We prove among other results: (1) If \(\pi\) : \(X\to X'\) is a proper open surjective morphism of complex spaces with X Kähler and X' reduced then, if either \(\pi\) is flat or X' normal, X' is Kähler. (2) If X is a Kähler space then the Barlet space \(B_ m(X)\) of compact complex m- cycles of X is Kähler. (3) Any reduced compact complex space in Fujiki's class \({\mathcal C}\) (holomorphic image of a compact Kähler space) is bimeromorphically equivalent to a compact Kähler manifold.
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 32C15
zbMATH DE Number: 4028354
zbMATH Keywords: proper open surjective morphism
zbMATH Keywords: complex spaces
zbMATH Keywords: Kähler space
zbMATH Keywords: Barlet space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4028354