TY - JOUR
T1 - On curves lying on a rational normal surface scroll
AU - Lee, Wanseok
AU - Park, Euisung
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
KW - Divisor
KW - Minimal free resolution
KW - Rational normal surface scroll
UR - http://www.scopus.com/inward/record.url?scp=85060897694&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85060897694&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2019.01.016
DO - 10.1016/j.jpaa.2019.01.016
M3 - Article
AN - SCOPUS:85060897694
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
ER -