The space of marked n distinct points on the complex projective line up to projective transformations will be called a configuration space. There are two families of complex hyperbolic structures on the configuration space constructed by Deligne Mostow and by Thurston. We review that these families are the same, and then exhibit the families for n = 4, 5 in constrast with the deformation theory of real hyperbolic cone 3-manifolds.
|Number of pages||15|
|Journal||Rendiconti dell'Istituto di Matematica dell'Universita di Trieste|
|Publication status||Published - 2001 Jan 1|
- Complex hyperbolic geometry
- Cone manifolds
- Configuration space
ASJC Scopus subject areas