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}
}