The strength of the Weak Lefschetz Property
Commutative Algebra
2009-12-02 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0803.3413,
title = {The strength of the Weak Lefschetz Property},
author = {Juan C. Migliore and Fabrizio Zanello},
journal= {arXiv preprint arXiv:0803.3413},
year = {2009}
}
Comments
A few minor corrections; to appear in the Illinois J. Math