On the Projective Structures Given by Theta

Given a compact Riemann surface $C$ and its Jacobian $J_{C}$, the line in $H^{0}(J_{C},\, 2\Theta )$ orthogonal to the sections of $2\Theta $ vanishing at $0\, \in \, J_{C}$ produces a natural projective structure on $C$. We investigate the properties of this projective structure.