New evidence for Green’s conjecture on syzygies of canonical curves
نویسندگان
چکیده
Some twelve years ago, Mark Green [G] made a few conjectures regarding the behaviour of syzygies of a curve C imbedded in IP n by a complete linear system. The so-called generic Green conjecture on canonical curves pertains to this question when the linear system is the canonical one and the curve is generic in the moduli, and predicts what are the numbers of syzygies in that case. Green and Lazarsfeld [GL] have observed that curves with nonmaximal Clifford index have extra syzygies and we will call specific Green conjecture on canonical curves the stronger prediction that the curves which have the numbers of syzygies expected for generic curves are precisely those with maximal Clifford index ([(g−1)/2]). (As a matter of fact, the full Green conjecture on canonical curves relates more closely the Clifford number with the existence of extra syzygies.) Many attempts have been made to settle this question, and some nice results have been obtained ([Sch][V]).
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