Author:
Almeida Charles,Andrade Aline V.
Abstract
Abstract
In [9], Migliore, Miró-Roig and Nagel proved that if
{R=\mathbb{K}[x,y,z]}
, where
{\mathbb{K}}
is a field of characteristic zero, and
{I=(L_{1}^{a_{1}},\dots,L_{4}^{a_{4}})}
is an ideal generated by powers of four general linear forms, then the multiplication by the square
{L^{2}}
of a general linear form L induces a homomorphism of maximal rank in any graded component of
{R/I}
. More recently, Migliore and Miró-Roig proved in [7] that the same is true for any number of general linear forms, as long the powers are uniform. In addition, they conjectured that the same holds for arbitrary powers. In this paper, we will prove that this conjecture is true, that is, we will show that if
{I=(L_{1}^{a_{1}},\dots,L_{r}^{a_{r}})}
is an ideal of R generated by arbitrary powers of any set of general linear forms, then the multiplication by the square
{L^{2}}
of a general linear form L induces a homomorphism of maximal rank in any graded component of
{R/I}
.
Funder
Fundação de Amparo à Pesquisa do Estado de São Paulo
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Subject
Applied Mathematics,General Mathematics
Reference28 articles.
1. The weak Lefschetz property and powers of linear forms in 𝕂[x,y,z]{\mathbb{K}[x,y,z]};Proc. Amer. Math. Soc.,2010
2. On the weak Lefschetz property for powers of linear forms;Algebra Number Theory,2012
3. Laplace equations and the weak Lefschetz property;Canad. J. Math.,2013
4. Weyl groups, the hard Lefschetz theorem, and the Sperner property;SIAM J. Algebr. Discrete Methods,1980
5. Weyl groups, the hard Lefschetz theorem, and the Sperner property;SIAM J. Algebr. Discrete Methods,1980
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