On the canonical ring of curves and surfaces
Algebraic Geometry
2011-07-05 v1
Abstract
Let C be a curve (possibly non reduced or reducible) lying on a smooth algebraic surface. We show that the canonical ring R(C, \omega_C) is generated in degree 1 if C is numerically 4-connected, not hyperelliptic and even (i.e. with K_C of even degree on every component). As a corollary we show that on a smooth algebraic surface of general type with p_g(S)>0 and q(S)=0 the canonical ring R(S, K_S) is generated in degree \leq 3 if there exists a curve C in |K_S| numerically 3-connected and not hyperelliptic.
Keywords
Cite
@article{arxiv.1107.0579,
title = {On the canonical ring of curves and surfaces},
author = {Marco Franciosi},
journal= {arXiv preprint arXiv:1107.0579},
year = {2011}
}