Projective curves of degree=codimension+2 II

Let C ⊂ ℙ^r be a nondegenerate projective integral curve of degree r + 1 which is not linearly normal. In this paper, we continues the study begun in [E. Park, Projective curves of degree=codimension+2, Math. Z. 256 (2007) 685-697] for the minimal free resolution of C. It is well-known that C is an isomorphic projection of a rational normal curve C˜ ⊂ ℙ^r+1 from a point P ∈ ℙ^r+1. Our main result is about how the graded Betti numbers of C are determined by the rank of P with respect to C˜, which is a measure of the relative location of P from C˜.