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
• Enlaces
  • Texto completo
• Resumen

  • We give a sharp lower bound for the Hilbert function in degree d of artinian quotients \Bbbk [x_1,\ldots ,x_n]/I failing the Strong Lefschetz property, where I is a monomial ideal generated in degree d \ge 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.

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