  We present gluing formulas for zeta regularized determinants of Dolbeault
laplacians on Riemann surfaces. These are expressed in terms of determinants of
associated operators on surfaces with boundary satisfying local elliptic
boundary conditions. The conditions are defined using the additional structure
of a framing, or trivialization of the bundle near the boundary. An application
to the computation of bosonization constants follows directly from these
formulas.
