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arXiv · 1905.09628

Cubic forms having matrix factorizations by Hessian matrices

Yeongrak Kim
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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 either one of four Severi varieties.

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Yeongrak Kim. 2019-05-23. Cubic forms having matrix factorizations by Hessian matrices. https://arxiv.org/abs/1905.09628

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