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Lefschetz Properties Of Some Codimension Three Artinian Gorenstein Algebras, Nancy Abdallah, Nasrin Altafi, Anthony Iarrobino, Alexandra Seceleanu, Joachim Yaméogo

Department of Mathematics: Faculty Publications

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 …