TY - JOUR
T1 - On curves lying on a rational normal surface scroll
AU - Lee, Wanseok
AU - Park, Euisung
N1 - Funding Information:
The first named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2017R1D1A1B03031438 ). The second named author was supported by the Korea Research Foundation Grant funded by the Korean Government ( NRF-2018R1D1A1B07041336 ).
Funding Information:
The first named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1B03031438). The second named author was supported by the Korea Research Foundation Grant funded by the Korean Government (NRF-2018R1D1A1B07041336).
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/10
Y1 - 2019/10
N2 - 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 )⊂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.
AB - 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 )⊂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.
KW - Divisor
KW - Minimal free resolution
KW - Rational normal surface scroll
UR - http://www.scopus.com/inward/record.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
VL - 223
SP - 4458
EP - 4476
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 10
ER -