Regularity and Multisecant Lines of Finite Schemes

Wanseok Lee; Euisung Park; Youngho Woo

doi:10.1093/imrn/rnx183

Regularity and Multisecant Lines of Finite Schemes

Wanseok Lee, Euisung Park, Youngho Woo

Department of Mathematics

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

Abstract

For a nondegenerate finite subscheme T in Pc , let reg(T) and λ(T) be, respectively, the regularity of T and the largest integer λ such that there exists an λ-secant line to T. It is always true that reg(T) = λ(T). In this article, we show that if reg(T) = d-c+5 2 then reg(T) is equal to λ(T). In addition, we describe the minimal free resolution of the homogeneous ideal of T for the case reg(T) = d-c+5 2 .

Original language	English
Article number	183
Pages (from-to)	1725-1743
Number of pages	19
Journal	International Mathematics Research Notices
Volume	2019
Issue number	6
DOIs	https://doi.org/10.1093/imrn/rnx183
Publication status	Published - 2019 Mar 22

ASJC Scopus subject areas

Mathematics(all)

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10.1093/imrn/rnx183

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title = "Regularity and Multisecant Lines of Finite Schemes",

abstract = "For a nondegenerate finite subscheme T in Pc , let reg(T) and λ(T) be, respectively, the regularity of T and the largest integer λ such that there exists an λ-secant line to T. It is always true that reg(T) = λ(T). In this article, we show that if reg(T) = d-c+5 2 then reg(T) is equal to λ(T). In addition, we describe the minimal free resolution of the homogeneous ideal of T for the case reg(T) = d-c+5 2 .",

author = "Wanseok Lee and Euisung Park and Youngho Woo",

note = "Funding Information: This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1B03031438) to W.L.; and Korea Research Foundation Grant funded by the Korean Government (NRF-2016R1D1A1A09918462) to E.P. Publisher Copyright: {\textcopyright} The Author(s) 2017.",

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AU - Park, Euisung

AU - Woo, Youngho

N1 - Funding Information: This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1B03031438) to W.L.; and Korea Research Foundation Grant funded by the Korean Government (NRF-2016R1D1A1A09918462) to E.P. Publisher Copyright: © The Author(s) 2017.

PY - 2019/3/22

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N2 - For a nondegenerate finite subscheme T in Pc , let reg(T) and λ(T) be, respectively, the regularity of T and the largest integer λ such that there exists an λ-secant line to T. It is always true that reg(T) = λ(T). In this article, we show that if reg(T) = d-c+5 2 then reg(T) is equal to λ(T). In addition, we describe the minimal free resolution of the homogeneous ideal of T for the case reg(T) = d-c+5 2 .

AB - For a nondegenerate finite subscheme T in Pc , let reg(T) and λ(T) be, respectively, the regularity of T and the largest integer λ such that there exists an λ-secant line to T. It is always true that reg(T) = λ(T). In this article, we show that if reg(T) = d-c+5 2 then reg(T) is equal to λ(T). In addition, we describe the minimal free resolution of the homogeneous ideal of T for the case reg(T) = d-c+5 2 .

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Regularity and Multisecant Lines of Finite Schemes

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