Abstract
In this paper, we study the minimal free resolution of non-ACM divisors X of a smooth rational normal surface scroll S=S(a1,a2)⊂Pr. Our main result shows that for a2≥2a1−1, 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.
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