26 research outputs found
A note on Jordan types and Jordan degree types
We discuss whether the Jordan degree type encodes \break more information
about graded artinian Gorenstein algebras than the Jordan type for linear
forms. We show that in codimension two, the Jordan type determines the Jordan
degree type. We provide examples showing that this is no longer the case in
higher codimensions
Monomial ideals and the failure of the Strong Lefschetz property
We give a sharp lower bound for the Hilbert function in degree of
artinian quotients failing the Strong Lefschetz
property, where is a monomial ideal generated in degree . We also
provide sharp lower bounds for other classes of ideals, and connect our result
to the classification of the Hilbert functions forcing the Strong Lefschetz
property by Zanello and Zylinski
Forcing the weak Lefschetz property for equigenerated monomial ideals
We classify the minimal number of generators of artinian equigenerated
monomial ideals such that is forced to have the
weak Lefschetz property.Comment: 27 page
Lefschetz properties of some codimension three Artinian Gorenstein algebras
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