On curves lying on a rational normal surface scroll

Wanseok Lee; Euisung Park

doi:10.1016/j.jpaa.2019.01.016

On curves lying on a rational normal surface scroll

Wanseok Lee, Euisung Park

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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)⊂P^r. 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.

Original language	English
Journal	Journal of Pure and Applied Algebra
DOIs	https://doi.org/10.1016/j.jpaa.2019.01.016
Publication status	Accepted/In press - 2019 Jan 1

Keywords

Divisor
Minimal free resolution
Rational normal surface scroll

ASJC Scopus subject areas

Algebra and Number Theory

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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.

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