The Gauss-Bonnet theorem for cone manifolds and volumes of moduli spaces

This paper generalizes the Gauss-Bonnet formula to a class of stratified spaces called Riemannian cone manifolds. As an application, we compute the volumes of the moduli spaces ${\cal M}_{0,n}$ with respect to the complex hyperbolic metrics introduced by Picard, Deligne-Mostow and Thurston.