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Let $\mathcal{O}$ be a closed orientable 2-orbifold of negative Eulercharacteristic. Huebschmann constructed the Atiyah-Bott-Goldman type symplecticform $\omega$ on the deformation space $\mathcal{C}(\mathcal{O})$ of convexprojective structures on $\mathcal{O}$. We show that the deformation space$\mathcal{C}(\mathcal{O})$ of convex projective structures on $\mathcal{O}$admits a global Darboux coordinates system with respect to $\omega$. To thisend, we show that $\mathcal{C}(\mathcal{O})$ can be decomposed into smallersymplectic spaces. In the course of the proof, we also study the deformationspace $\mathcal{C}(\mathcal{O})$ for an orbifold $\mathcal{O}$ with boundaryand construct the symplectic form on the deformation space of convex projectivestructures on $\mathcal{O}$ with fixed boundary holonomy.

Symplectic coordinates on the deformation spaces of convex projective structures on 2-orbifolds