The moduli space of \(n\)+1 points in complex hyperbolic \(n\)-space
type: Item
instance of: scholarly article
title: The moduli space of \(n\)+1 points in complex hyperbolic \(n\)-space
zbMATH Open document ID: 1026.51013
DOI: 10.1023/A:1023616007798
author: Jeffrey Hakim
author: Hanna Sandler
published in: Geometriae Dedicata
publication date: 2003-08-06T00:00:00Z
review text: They argue the \((n+1)\)-point configuration space in the complex hyperbolic \(n\)-space \(H^n_C\). They give a coordinate system on the moduli space \(\widetilde M\) with respect to the holomorphic isometry group \(PU (n,1)\). In the case \(n=2\), the result is well known result as shown by Brehm and by Cartan. The natural extension to the case \(n>2\) is obtained by natural suggestion and observation. The authors are interested in the moduli space \(M\) with respect to \(PU(n,1) \ltimes S_{n+1}\), where \(S_{n+1}\) is the symmetry group acting on \(n+1\) points. The results in this paper give good tools to investigate the topology type and singularity of \(M\).
reviewed by: Kazushi Ahara
Mathematics Subject Classification ID: 51M10
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 52B11
zbMATH DE Number: 1960039
zbMATH Keywords: complex hyperbolic geometry
zbMATH Keywords: \(n\)-dimensional polyhedra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1960039