A standard basis approach to syzygies of canonical curves.

Let C be a smooth projective curve of genus g defined over C and consider the canonical map cpK:C -> P'-* = P(H»(C9a>c)). is an embedding unless C is hyperelliptic. Moreover by a classical result of M. Noether the image of a nonhyperelliptic curve is projectively normal. In this paper we study the syzygies of the canonical curve C £j P'", i.e. the minimal free resolution 0 «_ Sc «S ^ F, «F2 «... «Fg_2 «0 of the homogeneous coordinate ring Sc = S/IC äs an S = C[x0, . . . , xg _ J-module. It is an easy consequence of Noether's result that ®S(-p-2y»*^ for /> = !,. . . ,#-3 i.e. that Fp is a module generated by elements in degree /? + ! and p + 2, and that /? _ 2 = S(— g — 1). Moreover the resolution is self-dual and satisfies