On the Koszul cohomology of canonical and Prym-canonical binary curves

In this paper we study Koszul cohomology and the Green and Prym-Green conjectures for canonical and Prym-canonical binary curves. We prove that, if property Np holds for a canonical or a Prym-canonical binary curve of genus g, then it holds for a generic canonical or Prymcanonical binary curve of genus g + 1. We also verify the Green and Prym-Green conjectures for generic canonical and Prym-canonical binary curves of low genus (6g15, g= 8 for Prym-canonical and 3g12 for canonical).