Green's Conjecture for curves on arbitrary K3 surfaces

Details Green's Conjecture for curves on arbitrary K3 surfaces Green's Conjecture for curves on arbitrary K3 surfaces

2009-11-27

arxiv.org/abs/0911.5310v3

Compositio Mathematica 147 (2011), 839-851

Mathematics

Algebraic Geometry

13 pages. Minor revisions, to appear in Compositio Mathematica

Scientific paper

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.

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