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Proceedings of the American Mathematical Society

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Cubic forms having matrix factorizations by Hessian matrices


Author: Yeongrak Kim
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
Published electronically: March 25, 2020
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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 one of the four Severi varieties.


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Yeongrak Kim
Affiliation: F. Mathematik und Informatik, Universität des Saarlandes, Campus E2.4, D-66123 Saarbrücken, Germany
Email: kim@math.uni-sb.de

DOI: https://doi.org/10.1090/proc/14993
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
Article copyright: © Copyright 2020 American Mathematical Society