  We derive the explicit form of the superpropagators in presence of general
boundary conditions (coisotropic branes) for the Poisson Sigma Model. This
generalizes the results presented in Cattaneo and Felder's previous works for
the Kontsevich angle function used in the deformation quantization program of
Poisson manifolds without branes or with at most two branes. The relevant
superpropagators for n branes are defined as gauge fixed homotopy operators of
a complex of differential forms on n sided polygons P_n with particular
"alternating" boundary conditions.
  In presence of more than three branes we use first order Riemann theta
functions with odd singular characteristics on the Jacobian variety of a
hyperelliptic Riemann surface (canonical setting). In genus g the
superpropagators present g zero modes contributions.
