Volumes of moduli spaces of hyperbolic surfaces with cone points

Abstract: In this paper we study volumes of moduli spaces of hyperbolic surfaces with geodesic, cusp and cone boundary components. We compute the volumes in some new cases, in particular when there exists a large cone angle. This allows us to give geometric meaning to Mirzakhani's polynomials under substitution of imaginary valued boundary lengths, corresponding to hyperbolic cone angles, and to study the behaviour of the volume under the $2\pi$ limit of a cone angle.