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

Hans-Christian v. Bothmer
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Abstract

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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Hans-Christian v. Bothmer. 2001-08-10. Geometric Syzygies of Canonical Curves of even Genus lying on a K3-Surface. https://arxiv.org/abs/math/0108078

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