  Let $K(X)$ denote the set of projective structures on a compact Riemann
surface $X$ whose holonomy representations are discrete. We will show that each
component of the interior of $K(X)$ is holomorphically equivalent to a complex
submanifold of the product of Teichm\"uller spaces and the holonomy
representation of every projective structure in the interior of $K(X)$ is a
quasifuchsian group.
