Abstract
A finite length graded R-module M has the Weak Lefschetz Property if there is a linear form ℓ in R such that the multiplication map ×ℓ:Mi→Mi+1 has maximal rank. The set of linear forms with this property form a Zariski-open set and its complement is called the non-Lefschetz locus. The main result is to give a complete proof for the theorem stated in [1] that for any general complete intersection I in R[x1,x2,x3,x4] the non-Lefschetz locus has expected codimension.
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