| We apply a degenerate version of a result of Hirschowitz, Ramanan and Voisin to verify Green and Green-Lazarsfeld conjectures over explicit open sets inside each d-gonal stratum of curves X with d < [g/2]+2. By the same method we verify Green-Lazarsfeld conjecture for any curve of odd genus and maximal gonality. The proof invokes Vosin's solution to the generic Green conjecture as a key argument. |