THE TWISTOR SPACE OF A 3-SASAKIAN MANIFOLD

Any compact 3-Sasakian manifold s is a principal circle V-bundle over a compact complex orbifold Z. This orbifold has a contact Fano structu re with a Kahler-Einstein metric of positive scalar curvature and it i s the twister space of a positive compact quaternionic Kahler orbifold O. We show that many results known to hold when Z is a smooth manifol d extend to this more general singular case. However, we construct inf inite families of examples with b(2)(Z) = 2 which sharply differs from the smooth case, where there is only one such Z.