Difference varieties and the Green-Lazarsfeld Secant Conjecture

The Green-Lazarsfeld Secant Conjecture is a generalization of Green’s Conjecture on syzygies of canonical curves to the cases of arbitrary line bundles. We establish the Green-Lazarsfeld Secant Conjecture for curves of genus g in all the divisorial case, that is, when the line bundles that fail to be (p+1)-very ample form a divisor in the Jacobian of the curve.