Green's Conjecture for curves on arbitrary K3 surfaces.
Gavril Farkas Marian Aprodu
posted in Mathematics on Sunday, November 29th, 2009
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 Vosin's results on syzygies of K3 sections, to the case of K3 surfaces with arbitrary Picard lattice. This, coupled with results of Vosin and Hirschowitz-Ramanan, provides a complete solution to Green's Conjecture for smooth curves on arbitrary K3 surfaces.
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