On curves lying on a rational normal surface scroll

Abstract

In this paper, we study the minimal free resolution of non-ACM divisors X of a smooth rational normal surface scroll S = S(a(1), a(2)) subset of P-r. Our main result shows that for a(2) >= 2a(1) - 1, there exists a nice decomposition of the Betti table of X as a sum of much simpler Betti tables. As a by-product of our results, we obtain a complete description of the graded Betti numbers of X for the cases where S = S(1, r - 2) for all r >= 3 and S = S(2, r - 3) for all r >= 6. (C) 2019 Elsevier B.V. All rights reserved.