Lefschetz properties of some codimension three Artinian Gorenstein algebras

Authors

Nancy Abdallah, University of Borås
Nasrin Altafi, KTH Royal Institute of Technology
Anthony Iarrobino, Northeastern University
Alexandra Seceleanu, University of Nebraska-LincolnFollow
Joachim Yaméogo, Université Côte d’Azur

Document Type

Article

Date of this Version

3-2-2022

Citation

arXiv:2203.01258v1 [math.AC] 2 Mar 2022

Comments

Used by permission.

Abstract

Codimension two Artinian algebras A have the strong and weak Lefschetz properties provided the characteristic is zero or greater than the socle degree. It is open to what extent such results might extend to codimension three AG algebras - the most promising results so far have concerned the weak Lefschetz property for such algebras. We here show that every standard-graded codimension three Artinian Gorenstein algebra A having low maximum value of the Hilbert function - at most six - has the strong Lefschetz property, provided that the characteristic is zero. When the characteristic is greater than the socle degree of A, we show that A is almost strong Lefschetz. This quite modest result is nevertheless arguably the most encompassing so far concerning the strong Lefschetz property for graded codimension three AG algebras.