Some notes and corrections of the paper ``The non-Lefschetz locus'' (Q6169044)

Let \(\pmb k\) be an algebraically closed field of characteristic zero and \(R\) be the polynomial ring \(\pmb k[x_1,x_2,x_3,x_4]\). The paper by \textit{M. Boij} et al. [J. Algebra 505, 288--320 (2018; Zbl 1393.13036)] proves that for general complete intersections of codimension four in \(R\), the non-Lefschetz locus has the expected codimension. The above theorem continues to hold; however the paper under review makes minor adjustments to some of the preliminary constructions from ``The non-Lefschetz locus''. The paper under review also includes a proof for a case that was not considered in ``The non-Lefschetz locus''. A finite length graded \(R\)-module \(M\) has the Weak Lefschetz Property if there is a linear form \(\ell\) in \(R\) such that the multiplication map \(\times \ell:M_i\to M_{i+1}\) 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.