  A key result for syzygies of curves is Voisin's proof of Green's conjecture
for the canonical embedding of a general curve of any genus. Her primary tools
were the Lazarsfeld Mukai bundle on a K3 surface and a representation of Koszul
cohomology on the Hilbert scheme of points on the surface. In this note we
construct representations of the Koszul complex on Grassmann varieties;
Voisin's setup arises as the inverse image of one of the maps. Using a
different map, we give a substantially shorter proof of Voisin's result for K3
surfaces of even sectional genus.
