Symplectic geometry of projective structures on surfaces with boundary

For oriented surfaces $\mathrm{\Sigma }$ with boundary, we consider the infinite-dimensional deformation space of projective structures on $\mathrm{\Sigma }$ with nondegenerate boundary, up to isotopies fixing the boundary. We show that this space carries a natural symplectic structure, and is a Hamiltonian space for the symplectic groupoid integrating the Adler-Gelfand-Dikii-space of the boundary.