On the Lefschetz locus in Gor(1,n,n,1)

2025/08/22 by Bezerra, Lenin, Ferrer, Viviana, Gondim, Rodrigo
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.16796

Abstract

We study two special families of cubic hypersurfaces with vanishing Hessian in ℙ^N, obtaining rational parametrizations and computing their degree in ℙ(S₃). For N ≤ 6, these two families exhaust the locus of cubics with vanishing Hessian that are not cones. As a consequence, via Macaulay-Matlis duality, we obtain a description of the locus in Gor(1, n, n, 1) corresponding to those algebras that satisfy the Strong Lefschetz property, for n ≤ 7.

Citations

• The Jordan type of graded Artinian Gorenstein algebras
• On cubic hypersurfaces with vanishing hessian
• Lefschetz elements of Artinian Gorenstein algebras and Hessians of homogeneous polynomials

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• Non-reduced components of the Noether-Lefschetz locus
• Polynomials with vanishing Hessian and Lefschetz properties