Harbourne, Schenck and Seceleanu's Conjecture

JOURNAL OF ALGEBRA

卷:462

Article

Miro-Roig, Rosa M.¹ 

[1] Fac Matemat, Dept Algebra & Geometria, Gran Via Corts Catalanes 585, Barcelona 08007, Spain

关键词: Weal Lefschetz property;    Powers of linear forms;    Artinian algebras;   

DOI  :  10.1016/j.jalgebra.2016.05.020

来源: Elsevier

【 摘 要 】

In [2], Conjecture 5.5.2, Harbourne, Schenck and Seceleanu conjectured that, for r = 6 and all r >= 8, the artinian ideal I = (l(1)(2),..., l(r+1)(2)) subset of K[x(1),...,x(r)] generated by the square of r+1 general linear forms l(i) fails the Weak Lefschetz property. This paper is entirely devoted to prove this Conjecture. It is worthwhile to point out that half of the Conjecture - namely, the case when the number of variables r is even - was already proved in [5], Theorem 6.1. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free