Castelnuovo–Mumford Regularity of Finite Schemes

Donghyeop Lee; Euisung Park

doi:10.1093/imrn/rnaf071

Castelnuovo–Mumford Regularity of Finite Schemes

Donghyeop Lee
, Euisung Park^*

^*Corresponding author for this work

Department of Mathematics

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

Abstract

Let Γ ⊂ Pⁿ be a nondegenerate finite subscheme of degree d. It is known that the Castelnuovo–Mumford regularity reg(Γ) of Γ is at most[FORMULA PRESENT]where t(Γ) is the smallest integer t such that Γ admits a (t + 2)-secant t-plane. In this paper, we show that reg(Γ) is close to the upper bound if and only if there exists a unique rational normal curve C of degree t(Γ) such that reg(Γ ∩ C) = reg(Γ).

Original language	English
Article number	rnaf071
Journal	International Mathematics Research Notices
Volume	2025
Issue number	6
DOIs	https://doi.org/10.1093/imrn/rnaf071
Publication status	Published - 2025 Mar 1

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© The Author(s) 2025. Published by Oxford University Press. All rights reserved.

ASJC Scopus subject areas

General Mathematics

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10.1093/imrn/rnaf071

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abstract = "Let Γ ⊂ Pn be a nondegenerate finite subscheme of degree d. It is known that the Castelnuovo–Mumford regularity reg(Γ) of Γ is at most[FORMULA PRESENT]where t(Γ) is the smallest integer t such that Γ admits a (t + 2)-secant t-plane. In this paper, we show that reg(Γ) is close to the upper bound if and only if there exists a unique rational normal curve C of degree t(Γ) such that reg(Γ ∩ C) = reg(Γ).",

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Castelnuovo–Mumford Regularity of Finite Schemes

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