Let X be an algebraic curve and c be the Clifford index of X. When c is small (e.g c=1), what is the classification of the line bundle who computes c?

Curves of Clifford index 1 (and some other small values) are classified. One should look at old papers written by Gerriet Martens 


when c= 0 Clifford's them includes the fact that any divisor with Clifford index 0 is a multiple of the hyperelliptic fiber, ie: a sum of fibers of the hyperelliptic map. If c=1 then the curve is either trigonal or a plane quintic I believe that it is an exercise in ACGH. Kind of a folk lore result. I have not heard of anyone explicating all the possible cases when c=2. 


I believe it has been known for a long time that Cliff = 2 occurs only for curves with either a g(1,4) or g(2,6), i.e. roughly 4  fold covers of P^1 or plane sextics. 

