Green's Conjecture for curves on arbitrary K3 surfaces
Algebraic Geometry
2014-01-14 v3
Abstract
Green's Conjecture predicts than one can read off special linear series on an algebraic curve, by looking at the syzygies of its canonical embedding. We extend Voisin's results on syzygies of K3 sections, to the case of K3 surfaces with arbitrary Picard lattice. This, coupled with results of Voisin and Hirschowitz-Ramanan, provides a complete solution to Green's Conjecture for smooth curves on arbitrary K3 surfaces.
Cite
@article{arxiv.0911.5310,
title = {Green's Conjecture for curves on arbitrary K3 surfaces},
author = {Marian Aprodu and Gavril Farkas},
journal= {arXiv preprint arXiv:0911.5310},
year = {2014}
}
Comments
13 pages. Minor revisions, to appear in Compositio Mathematica