  This paper considers curves in Grassmannians which are themselves immersed in
projective space by the Plucker map. It is shown that for a generic vector
bundle of high enough degree, the image curve lies in a proper linear
subvariety of this projective space and satisfies good conditions on syzygies
as a curve in this subspace. For very small degree and generic vector bundle,
the curve is non- degenerate.
