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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Cubic forms having matrix factorizations by Hessian matrices
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by Yeongrak Kim PDF
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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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