论文标题
在弱的Lefschetz属性上，几乎是由一般线性形式均匀产生的完整交叉点
On the weak Lefschetz property for almost complete intersections generated by uniform powers of general linear forms
论文作者
论文摘要
在2012年，第一作者Migliore和Nagel猜想，对于所有$ n \ geq 4 $，Artinian Ideal $ i =（l_0^d，\ ldots，l_ {2n+1}^d）当且仅当$ d> 1 $时，就没有弱的lefschetz属性。本文完全致力于部分猜想。更准确地说，我们证明$ r/i $无法拥有弱的lefschetz属性，提供了$ 4 \ leq n \ leq 8，\ d \ geq 4 $或$ d = 2r，\ 1 \ 1 \ 1 \ leq r \ leq 8，\ 4 \ 4 \ leq n \ leq n \ leq n \ leq 2r（r+2）-1 $。
In 2012, Migliore, the first author, and Nagel conjectured that, for all $n\geq 4$, the artinian ideal $I=(L_0^d,\ldots,L_{2n+1}^d) \subset R=k[x_0,\ldots,x_{2n}]$ 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 $4\leq n\leq 8,\ d\geq 4$ or $d=2r,\ 1\leq r\leq 8,\ 4\leq n\leq 2r(r+2)-1$.
