## Cubic forms having matrix factorizations by Hessian matrices

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- by Yeongrak Kim PDF
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**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.## References

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## Additional Information

**Yeongrak Kim**- Affiliation: F. Mathematik und Informatik, Universität des Saarlandes, Campus E2.4, D-66123 Saarbrücken, Germany
- MR Author ID: 1155792
- Email: kim@math.uni-sb.de
- Received by editor(s): May 29, 2019
- Received by editor(s) in revised form: October 14, 2019
- Published electronically: March 25, 2020
- Additional Notes: This work was supported by Project I.6 of SFB-TRR 195 “Symbolic Tools in Mathematics and their Application” of the German Research Foundation (DFG)
- Communicated by: Jerzy Weyman
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 2799-2809 - MSC (2010): Primary 13H10; Secondary 14E07, 17C20, 14J70
- DOI: https://doi.org/10.1090/proc/14993
- MathSciNet review: 4099769