%0 Journal Article
%T Geometric Syzygies of Canonical Curves of even Genus lying on a K3-Surface
%A Hans-Christian v. Bothmer
%J Mathematics
%D 2001
%I arXiv
%X Based on a recent result of Voisin [2001] we describe the last nonzero syzygy space in the linear strand of a canonical curve C of even genus g=2k lying on a K3 surface, as the ambient space of a k-2-uple embedded P^{k+1}. Furthermore the geometric syzygies constructed by Green and Lazarsfeld [1984] from g^1_{k+1}'s form a non degenerate configuration of finitely many rational normal curves on this P^{k+1}. This proves a natural generalization of Green's conjecture [1984], namely that the geometric syzygies should span the space of all syzygies, in this case.
%U http://arxiv.org/abs/math/0108078v1