Upper semicontinuity of automorphism groups
type: Item
instance of: scholarly article
title: Upper semicontinuity of automorphism groups
zbMATH Open document ID: 0827.32028
DOI: 10.1007/BF01459802
author: Buma Fridman
author: Evgeny A. Poletsky
published in: Mathematische Annalen
publication date: 1994-11-09T00:00:00Z
full work available at URL: https://eudml.org/doc/165226
review text: The authors prove striking results on upper semicontinuity of automorphism groups. They show, for example, that if pairs \((M_j, G_j)\) \((M_j\) connected complex manifolds and \(G_j\) subgroups of \(\Aut (M_j))\) converge on compacta to a pair \((M,G)\), where \(M\) is a hyperbolic complex manifold and \(G\) is a subgroup of \(\Aut (M)\), then \(G_j\) is isomorphic to \(G\) for large \(j\). They also show that any domain \(M\) in \(\mathbb{C}^n\) can be represented as a union of an increasing sequence of bounded domains \(M_k\) which admit \(\mathbb{Z}_k\) as automorphisms.
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 54H15
zbMATH DE Number: 683117
zbMATH Keywords: uniform convergence on compacta
zbMATH Keywords: Radon measures
zbMATH Keywords: upper semicontinuity
zbMATH Keywords: automorphism groups
reviewed by: Hassan Azad
MaRDI profile type: Publication
cites work: Q5605734
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description: scientific article; zbMATH DE number 683117