Abstract
We study the space C(a0,a1,…,an) of hyperbolic 2-spheres with cone points of prescribed apex curvatures 2a0,2a1,…,2an∈]0,2π[ and some related spaces. For n=3, we get a detailed description of such spaces. The euclidean 2-spheres were considered by W. P. Thurston: for n=4, the corresponding spaces provide the famous 7 examples of nonarithmetic compact holomorphic 2-ball quotients previously constructed by Deligne-Mostow.
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