  Let S be a compact connected oriented orbifold surface We show that using
Bers simultaneous uniformization, the moduli space of projective structure on S
can be mapped biholomorphically onto the total space of the holomorphic
cotangent bundle of the Teichm\"uller space for S. The total space of the
holomorphic cotangent bundle of the Teichm\"uller space is equipped with the
Liouville symplectic form, and the moduli space of projective structures also
has a natural holomorphic symplectic form. The above identification is proved
to be compatible with these symplectic structures. Similar results are obtained
for biholomorphisms constructed using uniformizations provided by Schottky
groups and Earle's version of simultaneous uniformization.
