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Research Article

On centres and direct sum decompositions of higher degree forms

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Pages 7290-7306 | Received 01 Aug 2021, Accepted 04 Sep 2021, Published online: 14 Oct 2021

References

  • Harrison D. A Grothendieck ring of higher degree forms. J Algebra. 1975;35:123–138.
  • Carlson J, Griffiths P. Infinitesimal variations of Hodge structure and the global Torelli problem. In: Beauville A, editor. Journées de Géometrie Algébrique d'Angers. Alphen aan den Rijn: Sijthoff and Noordhoff; 1980. p. 51–76.
  • Kleppe J. Additive splittings of homogeneous polynomials [Ph.D. thesis]. Oslo: University of Oslo; 2005. arXiv:1307.3532.
  • Prószyński A. On orthogonal decomposition of homogeneous polynomials. Fund Math. 1978;98:201–217.
  • Reichstein B. On symmetric operators of higher degree and their applications. Linear Algebra Appl. 1986;75:155–172.
  • Wang Z. On homogeneous polynomials determined by their Jacobian ideal. Manuscripta Math. 2015;146:559–574.
  • Buczyńska W, Buczyński J, Kleppe J, et al. Apolarity and direct sum decomposability of polynomials. Mich Math J. 2015;64:675–719.
  • Shafiei SM. Apolarity for determinants and permanents of generic matrices. J Commun Algebra. 2015;7:89–123.
  • Fedorchuk M. Direct sum decomposability of polynomials and factorization of associated forms. Proc Lond Math Soc. 2020;120(3):305–327.
  • Harrison D, Pareigis B. Witt rings of higher degree forms. Commun Algebra. 1988;16(6):1275–1313.
  • Keet A. Higher degree hyperbolic forms. Quaest Math. 1993;16:413–442.
  • O'Ryan M, Shapiro DB. Centers of higher degree forms. Linear Algebra Appl. 2003;371:301–314.
  • O'Ryan M, Shapiro DB. Centers of higher degree trace forms. J Pure Appl Algebra. 2013;217:2263–2273.
  • Pumplün S. Indecomposable forms of higher degree. Math Z. 2006;253:347–360.
  • Saxena N. On the centers of higher degree forms, unpublished article; 2005, posted at www.math.uni-bonn.de/people/saxena/papers/laa05.pdf
  • Donagi R. Generic Torelli for projective hypersurfaces. Compos Math. 1983;50:325–353.
  • Huang H-L, Lu H, Ye Y, et al. Diagonalizable higher degree forms and symmetric tensors. Linear Algebra Appl. 2021;613:151–169.
  • Mukai S. An introduction to invariants and moduli. Translated from the 1998 and 2000 Japanese editions by W. M. Oxbury. Cambridge: Cambridge University Press; 2003 (Cambridge studies in advanced mathematics, 81). xx + 503 pp.

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