The canonical ring of a 3-connected curve
Algebraic Geometry
2013-04-24 v2
Abstract
Let C be a projective curve either reduced with planar singularities or contained in a smooth algebraic surface. We show that the canonical ring R(C, \omega_C)= \oplus_{k \geq 0} H^0(C, \omega_C^k is generated in degree 1 if C is 3-connected and not (honestly) hyperelliptic; we show moreover that R(C, L)=\oplus_{k \geq 0} H^0(C,L^k)$ is generated in degree 1 if C is reduced with planar singularities and L is an invertible sheaf such that deg L_{|B} \geq 2p_a(B)+1 for every B \subseteq C.
Keywords
Cite
@article{arxiv.1107.5535,
title = {The canonical ring of a 3-connected curve},
author = {Marco Franciosi and Elisa Tenni},
journal= {arXiv preprint arXiv:1107.5535},
year = {2013}
}