Global, geometrical coordinates on Falbel's cross-ratio variety

Parker, John R.; Platis, Ioannis D.

Abstract

Falbel has shown that four pairwise distinct points on the boundary of a complex hyperbolic 2-space are completely determined, up to conjugation in PU(2,1), by three complex cross-ratios satisfying two real equations. We give global geometrical coordinates on the resulting variety.

Citation

Parker, J. R., & Platis, I. D. (2009). Global, geometrical coordinates on Falbel's cross-ratio variety. Canadian Mathematical Bulletin, 52(2), 285-294. https://doi.org/10.4153/cmb-2009-031-3

• Journal Article Type: Article
• Publication Date: May 1, 2009
• Deposit Date: Nov 6, 2009
• Journal: Canadian Mathematical Bulletin
• Print ISSN: 0008-4395
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 52
• Issue: 2
• Pages: 285-294
• DOI: https://doi.org/10.4153/cmb-2009-031-3
• Publisher URL: http://journals.cms.math.ca/cgi-bin/vault/view/parkerB8962