Developable cubics in ${\mathbb{P}}^4$ and the Lefschetz locus in $\mathrm{GOR}(1,5,5,1)$

Abstract

We provide a classification of developable cubic hypersurfaces in ${\mathbb{P}}^4$. Using the correspondence between forms of degree $3$ on ${\mathbb{P}}^4$ and Artinian Gorenstein $\mathbb{K}$-algebras, given by Macaulay-Matlis duality, we describe the locus in $\mathrm{GOR}(1,5,5,1)$ corresponding to those algebras which satisfy the Strong Lefschetz property.

22 pages, 1 figure