Gonality, Clifford index and multisecants

The gonality of a projective curve C is the minimal degree of a morphism f : C→P1. It is a classical invariant which has been refined by the introduction of the Clifford index. If Csubset ofP3 is a smooth, connected curve, Gon(C) is said to be computable by multisecants if Gon(C)=deg(C)−l where l is the highest order of a multisecant to C. In this paper we prove that the gonality is computable by multisecants and that Cliff(C)=Gon(C)−2 for most subcanonical curves in P3. We also describe the stratification by multisecants of the Hilbert schemes of complete intersections and rational curves.