The moduli space of complex geodesics in the complex hyperbolic plane.

Abstract

We consider the space M of ordered m-tuples of distinct complex geodesics in complex hyperbolic 2-space, H2 C, up to its holomorphic isometry group PU(2, 1). One of the important problems in complex hyperbolic geometry is to construct and describe the moduli space for M. This is motivated by the study of the deformation space of groups generated by reflections in complex geodesics. In the present paper, we give the complete solution to this problem.