Lefschetz elements of Artinian Gorenstein algebras and Hessians of homogeneous polynomials
By Toshiaki Maeno, Junzo Watanabe. 2009
105 citations recorded by the source corpus.
We give a characterization of the Lefschetz elements in Artinian Gorenstein rings over a field of characteristic zero in terms of the higher Hessians. As an application, we give new examples of Artinian Gorenstein rings which do not have the strong Lefschetz property.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/50cf62ee3e3ca38281faa7574244146332440c30
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- On higher Hessians and the Lefschetz properties (2015, methodology): “ntically. The vanishing of higher Hessians is closely related with the Strong (or Weak) Lefschetz property for standard graded Artinian Gorenstein algebra, as pointed out firstly in [Wa2] and later in [MW]. As an application we construct for each pair (N.d) 6= (3 ,3),(3,4) infinitely many standard gra”