The Moduli Space of Points in the Boundary of Complex Hyperbolic Space

@article{Cunha2012TheMS,
  title={The Moduli Space of Points in the Boundary of Complex Hyperbolic Space},
  author={Heleno Cunha and Nikolay Gusevskii},
  journal={Journal of Geometric Analysis},
  year={2012},
  volume={22},
  pages={1-11}
}
We consider the space $\mathcal{M}(n,m)$ of ordered m-tuples of distinct points in the boundary of complex hyperbolic n-space, $\mathbf{H}_{\mathbb{C}}^{n}$, up to its holomorphic isometry group PU(n,1). An important problem in complex hyperbolic geometry is to construct and describe the moduli space for $\mathcal{M}(n,m)$. In particular, this is motivated by the study of the deformation space of complex hyperbolic groups generated by loxodromic elements. In the present paper, we give the… CONTINUE READING