The PU(2,1) configuration space of four points in S3 and the cross-ratio variety

The configuration space of four points on the standard CR 3-sphere up to CR-automorphisms is a real four dimensional variety. We prove the existence of natural complex and CR structures on this space.

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Bibliographic Details
Published inMathematische annalen Vol. 340; no. 4; pp. 935 - 962
Main Authors Falbel, Elisha, Platis, Ioannis D.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 2008
Subjects
Mathematics
Mathematics and Statistics
Levi Form
Exact Sequence
Heisenberg Group
Quotient Space
Diagonal Action
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Summary:The configuration space of four points on the standard CR 3-sphere up to CR-automorphisms is a real four dimensional variety. We prove the existence of natural complex and CR structures on this space.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-007-0177-0