The weak Lefschetz property of equigenerated monomial ideals

JOURNAL OF ALGEBRA

卷:556

Article

Altafi, Nasrin¹  Boij, Mats¹ 

[1] KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

关键词: Weak Lefschetz property;    Monomial ideals;    Group actions;   

DOI  :  10.1016/j.jalgebra.2020.02.020

来源: Elsevier

【 摘 要 】

We determine a sharp lower bound for the Hilbert function in degree d of a monomial algebra failing the weak Lefschetz property over a polynomial ring with n variables and generated in degree d, for any d >= 2 and n >= 3. We consider artinian ideals in the polynomial ring with n variables generated by homogeneous polynomials of degree d invariant under an action of the cyclic group Z/dZ, for any n >= 3 and any d >= 2. We give a complete classification of such ideals in terms of the weak Lefschetz property depending on the action. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free