Illinois Journal of Mathematics

The strength of the Weak Lefschetz Property

Juan Migliore and Fabrizio Zanello

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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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Illinois J. Math., Volume 52, Number 4 (2008), 1417-1433.

First available in Project Euclid: 18 November 2009

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Primary: 13E10: Artinian rings and modules, finite-dimensional algebras 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05] 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series


Migliore, Juan; Zanello, Fabrizio. The strength of the Weak Lefschetz Property. Illinois J. Math. 52 (2008), no. 4, 1417--1433. doi:10.1215/ijm/1258554370.

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