Syzygies of canonical curves and special linear series (Q1066206)

The syzygies of canonical curves C are related to the existence of special linear series \(g^ r_ d\) on C. For curves C of genus \(g=7\) or \(g=8\) the values of the graded Betti-numbers depend on and determine the existence of a \(g^ 1_ 2, g^ 1_ 3, g^ 2_ 6\) or \(g^ 1_ 4\) on C. This result verifies a conjecture of M. Green for canonical curves of genus \(g\leq 8\) over a field k of \(char(k)=0\).