Lefschetz properties for jacobian rings of cubic fourfolds and other Artinian algebras

Bricalli, Davide ^[1] ; Favale. Filippo Francesco ^[2]
1. [1] University of Milano-Bicocca
  
  University of Milano-Bicocca
  
  Milán, Italia
2. [2] University of Pavia
  
  University of Pavia
  
  Pavía, Italia
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 1, 2024, págs. 149-169
Idioma: inglés
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Resumen
- In this paper, we exploit some geometric-differential techniques to prove the strong Lefschetz property in degree 1 for a complete intersection standard Artinian Gorenstein algebra of codimension 6 presented by quadrics. We prove also some strong Lefschetz properties for the same kind of Artinian algebras in higher codimensions. Moreover, we analyze some loci that come naturally into the picture of “special” Artinian algebras: for them we give some geometric descriptions and show a connection between the non emptiness of the so-called non-Lefschetz locus in degree 1 and the “lifting” of a weak Lefschetz property to an algebra from one of its quotients.