### 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 |
---|---|

Journal | Journal of Pure and Applied Algebra |

DOIs | |

Publication status | Accepted/In press - 2019 Jan 1 |

### Fingerprint

### Keywords

- Divisor
- Minimal free resolution
- Rational normal surface scroll

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**On curves lying on a rational normal surface scroll.** / Lee, Wanseok; Park, Euisung.

Research output: Contribution to journal › Article

}

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 -