COHERENT SYSTEMS OF GENUS 0 II: EXISTENCE RESULTS FOR k ≥ 3

In this paper, we continue the investigation of coherent systems of type (n,d,k) on the projective line which are stable with respect to some value of a parameter α. We work mainly with k < n and obtain existence results for arbitrary k in certain cases, together with complete results for k = 3. Our methods involve the use of the "flips" which occur at critical values of the parameter.