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.

Bricalli, D., Favale, F. (2024). Lefschetz properties for jacobian rings of cubic fourfolds and other Artinian algebras. COLLECTANEA MATHEMATICA, 75(1), 149-169 [10.1007/s13348-022-00382-5].

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

Bricalli, D;Favale, FF
2024

Abstract

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.
Articolo in rivista - Articolo scientifico
Artinian Gorenstein algebras; Complete intersections; Cubic fourfolds; Jacobian rings; Lefschetz properties;
English
19-nov-2022
2024
75
1
149
169
open
Bricalli, D., Favale, F. (2024). Lefschetz properties for jacobian rings of cubic fourfolds and other Artinian algebras. COLLECTANEA MATHEMATICA, 75(1), 149-169 [10.1007/s13348-022-00382-5].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/402217
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