The strength of the Weak Lefschetz Property

Details The strength of the Weak Lefschetz Property The strength of the Weak Lefschetz Property

2008-03-24

arxiv.org/abs/0803.3413v2

Illinois J. Math. 52 (2008), no. 4, 1417-1433

Mathematics

Commutative Algebra

A few minor corrections; to appear in the Illinois J. Math

Scientific paper

We study a number of conditions on the Hilbert function of a level artinian algebra which imply the Weak Lefschetz Property (WLP). Possibly the most important open case is whether a codimension 3 SI-sequence forces the WLP for level algebras. In other words, does every codimension 3 Gorenstein algebra have the WLP? We give some new partial answers to this old question: we prove an affirmative answer when the initial degree is 2, or when the Hilbert function is relatively small. Then we give a complete answer to the question of what is the largest socle degree forcing the WLP.

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