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Global Geometrical Coordinates on Falbel's Cross-Ratio Variety

  Published:2009-06-01
 Printed: Jun 2009
  • John R. Parker
  • Ioannis D. Platis
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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, 32M05 show english descriptions Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]
Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]
32G05 - Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]
32M05 - Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]
 

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