Monomial ideals and the failure of the Strong Lefschetz property

Altafi, Nasrin ^[1] ; Lundqvist, Samuel ^[2]
1. [1] Royal Institute of Technology
  
  Royal Institute of Technology
  
  Suecia
2. [2] Stockholm University
  
  Stockholm University
  
  Suecia
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 73, Fasc. 3, 2022, págs. 383-390
Idioma: inglés
DOI: 10.1007/s13348-021-00324-7
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Resumen
- We give a sharp lower bound for the Hilbert function in degree d of artinian quotients k[x1,…,xn]/I failing the Strong Lefschetz property, where I is a monomial ideal generated in degree d≥2. We also provide sharp lower bounds for other classes of ideals, and connect our result to the classification of the Hilbert functions forcing the Strong Lefschetz property by Zanello and Zylinski.