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

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

1 Citation (Scopus)

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
Pages (from-to)	4458-4476
Number of pages	19
Journal	Journal of Pure and Applied Algebra
Volume	223
Issue number	10
DOIs	https://doi.org/10.1016/j.jpaa.2019.01.016
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

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10.1016/j.jpaa.2019.01.016

Cite this

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title = "On curves lying on a rational normal surface scroll",

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.",

keywords = "Divisor, Minimal free resolution, Rational normal surface scroll",

author = "Wanseok Lee and Euisung Park",

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: {\textcopyright} 2019 Elsevier B.V.",

year = "2019",

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doi = "10.1016/j.jpaa.2019.01.016",

language = "English",

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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.

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ER -

On curves lying on a rational normal surface scroll

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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