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This article follow the article{http://hal.archives-ouvertes.fr/hal-00361030/fr/} in which the authorcharacterize the fact of being of finite volume for a convex projectivesurface. We show here that the moduli space $\beta_f(\Sigma_{g,p})$ of theconvex projective structure on the surface $\Sigma_{g,p}$ of genius $g$ with$p$ punctures is homeomorphic to $\R^{16g-16+6p}$. Finally, we show that$\beta_f(\Sigma_{g,p})$ can be identify with a connected component of the spaceof representation of the fundamental group of $\Sigma_{g,p}$ in $SL(3,R)$ whichkeep the parabolic modulo conjugaison.

Espace de Modules Marques des Surfaces Projectives Convexes de Volume Fini