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.

Comment: 12 pages. Final version, to appear in the Epiga volume dedicated to Claire Voisin

• 14H10 - Families, moduli of curves (algebraic)
• 14H60 - Vector bundles on curves and their moduli