The gonality of complete intersection curves

The purpose of this paper is to show that for a complete intersection curve C in projective space (other than a few exceptions stated below), any morphism f : C -> P-r satisfying deg f* O-Pr (1) < deg C is obtained by projection from a linear space. In particular, we obtain bounds on the gonality of such curves and compute the gonality of general complete intersection curves. We also prove a special case of one of the well-known Cayley-Bacharach conjectures posed by Eisenbud, Green, and Harris. Published by Elsevier Inc.