On the rigidity of certain discrete groups and algebraic varieties
type: Item
instance of: scholarly article
title: On the rigidity of certain discrete groups and algebraic varieties
zbMATH Open document ID: 0624.32019
DOI: 10.1007/BF01458080
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164301
review text: A rigidity result in the class of Kähler varieties is derived for locally symmetric complex spaces of finite volume and rank\(\geq 2\), as well as for the moduli space of Riemann surfaces of genus \(g\geq 2\). If a Kähler variety admits a compactification of complex codimension at least three and is homotopically equivalent to one of these model spaces, then it is already \(\pm\) biholomorphically equivalent to the model. Our construction uses harmonic maps in a crucial way.
Mathematics Subject Classification ID: 32N15
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 32J05
zbMATH DE Number: 4013030
zbMATH Keywords: discrete automorphism group
zbMATH Keywords: Teichmüller space
zbMATH Keywords: modular group
zbMATH Keywords: rigidity
zbMATH Keywords: locally symmetric complex spaces
zbMATH Keywords: moduli space of Riemann surfaces
zbMATH Keywords: Kähler variety
zbMATH Keywords: compactification
zbMATH Keywords: homotopically equivalent
zbMATH Keywords: biholomorphically equivalent
zbMATH Keywords: harmonic maps
author: Jürgen Jost
author: Shing-Tung Yau
MaRDI profile type: Publication
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OpenAlex ID: W1988747202
description: scientific article; zbMATH DE number 4013030