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Oberseminar WiSe 12/13 Zusammenfassung des Vortrags von Paola Frediani

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

I will report on a joint work with Elisabetta Colombo on the Koszul cohomology and the Green and Prym-Green conjectures for canonical and Prym-canonical binary curves. I will describe explicit canonical and Prym-canonical models of binary curves to show that if property N_p holds for a canonical or Prym-canonical binary curve of genus g, then it holds for a generic canonical or Prym-canonical binary curve of genus g+1. These models also allow us to make explicit computations to verify the Green and Prym-Green conjectures for generic canonical and Prym-canonical binary curves of low genus.