SLP in the studied settings

Determine whether the Artinian algebras R/A_{X,d} considered in this work—specifically those defined by d-th powers of linear forms dual to points on an a × a grid in P^3 (for 1 ≤ d ≤ a − 1 and for d a multiple of a − 1), on a × b grids with b > a and d ≥ a, and on (a, b)-geproci sets—satisfy the Strong Lefschetz Property.

Background

The Strong Lefschetz Property (SLP) strengthens WLP by requiring that multiplication by powers of a general linear form have maximal rank in every degree. The paper resolves WLP for square grids and conjectures systematic WLP failure for non-square grids with large d, but it does not address SLP.

This question asks whether SLP holds in the same families, including both proven-WLP and conjectural-failure regimes, thereby extending the scope of Lefschetz properties examined in the paper.