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.
Citation
Juan Migliore. Fabrizio Zanello. "The strength of the Weak Lefschetz Property." Illinois J. Math. 52 (4) 1417 - 1433, Winter 2008. https://doi.org/10.1215/ijm/1258554370
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