The strength of the Weak Lefschetz Property
Juan Migliore and Fabrizio Zanello
Source: Illinois J. Math. Volume 52, Number 4
(2008), 1417-1433.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.ijm/1258554370
Zentralblatt MATH identifier: 1178.13011
Mathematical Reviews number (MathSciNet): MR2595775
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