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On the Koszul cohomology of canonical and Prym‐canonical binary curves
Author(s) -
Colombo Elisabetta,
Frediani Paola
Publication year - 2013
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdt033
Subject(s) - mathematics , binary number , pure mathematics , canonical form , genus , cohomology , arithmetic , botany , biology
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 N p 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).