Symplectic Coordinates on the Deformation Spaces of Convex Projective Structures on 2-Orbifolds

Let O be a closed orientable 2-orbifold of negative Euler characteristic. Huebschmann constructed the Atiyah-Bott-Goldman type symplectic form ω on the deformation space C (O) of convex projective structures on O. We show that the deformation space C (O) of convex projective structures on O admits a global Darboux coordinate system with respect to ω . To this end, we show that C (O) can be decomposed into smaller symplectic spaces. In the course of the proof, we also study the deformation space C (O) for an orbifold O with boundary and construct the symplectic form on the deformation space of convex projective structures on O with fixed boundary holonomy.