Bulletin of the
Korean Mathematical Society BKMS

Let $C \subset \P^r$ 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 $d \leq 2r-2$ and $C$ is contained in a rational normal surface scroll. Our main result provides all the graded Betti numbers of $C$ explicitly.

Keywords: curve of maximal regularity, minimal free resolution

MSC numbers: Primary 14H45; Secondary 13D02