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Global Geometrical Coordinates on Falbel's Cross-Ratio Variety |
Canad. Math. Bull. 52(2009), 285-294
E-Published:
2009-06-01
Printed: Jun 2009
Printed: Jun 2009
- John R. Parker
- Ioannis D. Platis
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.
| 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] |