On the Weak-Lefschetz property for Artinian Gorenstein algebras

Details On the Weak-Lefschetz property for Artinian Gorenstein algebras On the Weak-Lefschetz property for Artinian Gorenstein algebras

2011-12-07

arxiv.org/abs/1112.1498v1

Mathematics

Commutative Algebra

Scientific paper

We deal with the Weak Lefschetz property (WLP) for Artinian standard graded Gorenstein algebras of codimension $3.$ We prove that many Gorenstein sequences force the WLP for such algebras. Moreover for every Gorenstein sequence $H$ of codimension 3 we found several Gorenstein Betti sequences compatible with $H$ which again force the WLP. Finally we show that for every Gorenstein Betti sequence the general Artinian standard graded Gorenstein algebra with such Betti sequence has the WLP.

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