Geometric Syzygies of Canonical Curves of even Genus lying on a K3-Surface

Details Geometric Syzygies of Canonical Curves of even Genus lying on a K3-Surface Geometric Syzygies of Canonical Curves of even Genus lying on a K3-Surface

2001-08-10

arxiv.org/abs/math/0108078v1

Mathematics

Algebraic Geometry

29 pages; 5 figures

Scientific paper

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.

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