ON THE MINIMAL FREE RESOLUTION OF CURVES OF MAXIMAL REGULARITY

Abstract

Let C subset of P-r be a nondegenerate projective curve of degree d > r + 1 and of maximal regularity. Such curves are always contained in the threefold scroll S(0, 0, r - 2). Also some of such curves are even contained in a rational normal surface scroll. In this paper we study the minimal free resolution of the homogeneous coordinate ring of C in the case where d <= 2r - 2 and C is contained in a rational normal surface scroll. Our main result provides all the graded Betti numbers of C explicitly.