On the weak Lefschetz property for almost complete intersections generated by uniform powers of general linear forms

JOURNAL OF ALGEBRA

卷:551

Article

Miro-Roig, Rosa M.¹  Quang Hoa Tran² 

[1] Univ Barcelona, Dept Matemat & Informat, Gran Via Corts Catalanes 585, E-08007 Barcelona, Spain

[2] Hue Univ, Univ Educ, 34 Le Loi St, Hue City, Vietnam

关键词: Almost complete intersections;    Artinian algebras;    General linear forms;    Linear systems of general points;    Powers of linear forms;    Weak Lefschetz property;   

DOI  :  10.1016/j.jalgebra.2019.12.029

来源: Elsevier

【 摘 要 】

In [10], Conjecture 6.6, Migliore, the first author, and Nagel conjectured that, for all n >= 4, the artinian ideal I = (L-0(d), ..., L-2n+1(d)) subset of R = k[x(0), ..., x(2n)] generated by the d-th powers of 2n + 2 general linear forms fails to have the weak Lefschetz property if and only if d > 1. This paper is entirely devoted to prove partially this conjecture. More precisely, we prove that R/I fails to have the weak Lefschetz property, provided 4 <= n <= 8, d >= 4 or d = 2r, 1 <= r <= 8, 4 <= n <= 2r(r + 2) - 1. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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