The non-Lefschetz locus of vector bundles of rank 2 over [formula omitted

Abstract

A finite length graded R-module M has the Weak Lefschetz Property if there is a linear element ℓ in R such that the multiplication map ×ℓ:Mt→Mt+1 has maximal rank for every integer t. The set of linear forms with this property form a Zariski-open set and its complement is called the non-Lefschetz locus. In this paper we study the non-Lefschetz locus for the first cohomology module H⁎1(P2,E) of a vector bundle E of rank 2 over P2. The main result is to show that this non-Lefschetz locus has the expected codimension under the assumption that E is general.