The syzygies of a generic canonical curve are expected to be as simple as possible for p≤(g−3)/2. We prove this result here for p≤(g−2)/3 only. The proof is carried out by considering infinitesimal deformations near a hyperelliptic curve.
"Green's conjecture for the generic r-gonal curve of genus g≥3r−7." Duke Math. J. 111 (2) 195 - 222, 1 February 2002. https://doi.org/10.1215/S0012-7094-02-11121-1