The moduli space of hyperbolic compact complex spaces
type: Item
instance of: scholarly article
title: The moduli space of hyperbolic compact complex spaces
zbMATH Open document ID: 1126.32008
author: Adel Khalfallah
published in: Mathematische Zeitschrift
publication date: 2007-09-11T00:00:00Z
review text: The author constructs the moduli space of reduced hyperbolic compact complex spaces. He uses a general criterion to represent analytic functors by coarse moduli spaces. This criterion has already been used to construct the moduli space of polarized Kähler manifolds. In the first part of the paper one proves that the property of Landau holds also for complex spaces and not only for manifolds or for complex spaces with isolated singularities. After recalling the criterion allowing to represent analytic functors by coarse moduli spaces, the author proves that for any two families \(\mathcal{X}\to S\) and \(\mathcal{Y}\to S\) of reduced hyperbolic compact complex spaces parametrized by a complex space \(S\), the natural map \(\text{Bim}_S(\mathcal{X},\mathcal{Y})\to S\) is proper. Next, he considers two types of families of deformations: the first one is a family of locally trivial deformations, the second one is simultaneous resolutions of singularities.
reviewed by: Vasile Oproiu
Mathematics Subject Classification ID: 32G13
Mathematics Subject Classification ID: 32Q45
Mathematics Subject Classification ID: 53C56
Mathematics Subject Classification ID: 32F45
Mathematics Subject Classification ID: 14D22
Mathematics Subject Classification ID: 32S45
zbMATH DE Number: 5189576
zbMATH Keywords: moduli space
zbMATH Keywords: hyperbolic compact complex spaces
zbMATH Keywords: Kobayashi-Royden pseudo-metrics
zbMATH Keywords: property of Landau
MaRDI profile type: Publication
full work available at URL: s00209-006-0036-9
OpenAlex ID: W2085059745
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DOI: 10.1007/S00209-006-0036-9
description: scientific article; zbMATH DE number 5189576