English

On Clifford's theorem for singular curves

Algebraic Geometry 2014-02-26 v2

Abstract

Let C be a 2-connected Gorenstein curve either reduced or contained in a smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dim scheme such that the space H^0(C, I_S K_C) contains a generically invertible section). Under some general assumptions on S or C we show that h^0(C, I_S K_C) <= p_a(C) - deg (S)/2 and if equality holds then either S is trivial, or C is honestly hyperelliptic or 3-disconnected. As a corollary we give a generalization of Clifford's theorem for reduced curves.

Keywords

Cite

@article{arxiv.1105.2253,
  title  = {On Clifford's theorem for singular curves},
  author = {Marco Franciosi and Elisa Tenni},
  journal= {arXiv preprint arXiv:1105.2253},
  year   = {2014}
}
R2 v1 2026-06-21T18:05:51.147Z