location:  Publications → journals → CMB
Abstract view

# Global Geometrical Coordinates on Falbel's Cross-Ratio Variety

Published:2009-06-01
Printed: Jun 2009
• John R. Parker
• Ioannis D. Platis
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
 Format: HTML LaTeX MathJax PDF PostScript

## 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 ${\rm PU}(2,1)$, by three complex cross-ratios satisfying two real equations. We give global geometrical coordinates on the resulting variety.
 MSC Classifications: 32G05 - Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15] 32M05 - Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]