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

Abstract

In 2012, Migliore, the first author, and Nagel conjectured that, for all $n\ge 4$, the artinian ideal $I=(L_0^d,\dots ,L_{2n+1}^d)\subset R=k[x_0,\dots ,x_{2n}]$ 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 $4\le n\le 8,d\ge 4$ or $d=2r,1\le r\le 8,4\le n\le 2r(r+2)-1$.

To appear in Journal of Algebra. 20 pages

Cited by in corpus (3)

• The weak Lefschetz property for Artinian Gorenstein algebras of codimension three
• A classification of the weak Lefschetz property for almost complete intersections generated by uniform powers of general linear forms
• The weak Lefschetz property of Gorenstein algebras of codimension three associated to the Apéry sets