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 )⊂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.
Original language | English |
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Pages (from-to) | 4458-4476 |
Number of pages | 19 |
Journal | Journal of Pure and Applied Algebra |
Volume | 223 |
Issue number | 10 |
DOIs | |
Publication status | Published - 2019 Oct |
Bibliographical note
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.
Keywords
- Divisor
- Minimal free resolution
- Rational normal surface scroll
ASJC Scopus subject areas
- Algebra and Number Theory