GONALITY OF A GENERAL ACM CURVE IN P3

Let C be an ACM (projectively normal) nonsingular curve in P-C(3) not contained in a plane, and suppose C is general in its Hilbert scheme-this is irreducible once the postulation is fixed. Answering a question posed by Peskine, we show the gonality of C is d - l, where d is the degree of the curve and l is the maximum order of a multisecant line of C. Furthermore l = 4 except for two series of cases, in which the postulation of C forces every surface of minimum degree containing C to contain a line as well. We compute the value of l in terms of the postulation of C in these exceptional cases. We also show the Clifford index of C is equal to gon(C) - 2.