Some notes and corrections of the paper "The non-Lefschetz locus".

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 : M i → M i + 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 [ x 1 , x 2 , x 3 , x 4 ] the non-Lefschetz locus has expected codimension. [ABSTRACT FROM AUTHOR]