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

Thiago Fassarella; Viviana Ferrer; Rodrigo Gondim

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arXiv · 2002.08995

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

Thiago Fassarella·Viviana Ferrer·Rodrigo Gondim

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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 ${\rm GOR}(1,5,5,1)$ corresponding to those algebras which satisfy the Strong Lefschetz property.

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Thiago Fassarella, Viviana Ferrer, Rodrigo Gondim. 2020-02-20. Developable cubics in $\mathbb P^4$ and the Lefschetz locus in ${\rm GOR}(1,5,5,1)$. https://arxiv.org/abs/2002.08995

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