On the Koszul cohomology of canonical and Prym-canonical binary curves
Abstract
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 Prym-canonical 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 (6≤ g≤ 15, g≠ 8 for Prym-canonical and 3≤ g≤ 12 for canonical).
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