Cubic forms having matrix factorizations by Hessian matrices

Kim, Yeongrak

doi:10.1090/proc/14993

Cubic forms having matrix factorizations by Hessian matrices
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Proc. Amer. Math. Soc. 148 (2020), 2799-2809 Request permission

Abstract:

Using a part of XJC-correspondence by Pirio and Russo, we classify cubic forms $f$ whose Hessian matrices induce matrix factorizations of themselves. When it defines a reduced hypersurface, it satisfies the “secant–singularity” correspondence, that is, it coincides with the secant locus of its singular locus. In particular, when $f$ is irreducible, its singular locus is one of the four Severi varieties.

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