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

Abstract

In [11], Conjecture 6.6, Migliore, the first author, and Nagel conjectured that, for all n ≥ 4, the artinian ideal. , 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.

The weak Lefschetz property of graded Gorenstein algebras associated to the Apéry set of a numerical semigroup

“…Most authors have studied the problem from different points of view, applying tools from representation theory, topology, vector bundle theory, plane partitions, differential geometry, among others (see for instance [1][2][3][4][5][6][7][8][9]).…”

Case of misdiagnosed melioidosis from Hue city, Vietnam

“…The study of Lefschetz properties of graded algebras has connections to several areas of mathematics. Many authors have studied the problem from many different points of view, applying tools from representation theory, algebraic topology, differential geometry, commutative algebra, among others (see, for instance, [6,16,22,25,26,27,28,29,30,31,32,33,36]). Even the characteristic of k plays an interesting role in the study of the Lefschetz properties; see, for example, [7,8,9,20,21,27].…”