The non-Lefschetz locus of vector bundles of rank 2 over ℙ²

2021/10/05 by Marangone, Emanuela
#13A02 #13C40 #13D02 (primary) 13H10 #13E10 #13F20 #14F06 (secondary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.02377

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: 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. In this paper we focus on the study of the non-Lefschetz locus for the first cohomology module H_*¹(ℙ²,E) of a locally free sheaf 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.

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