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SYMMETRIC TENSOR RANK, CACTUS RANK AND RELATED COMPLEXITY MEASURES FOR HOMOGENEOUS POLYNOMIALS

Year 2014, , 126 - 132, 30.04.2014
https://doi.org/10.36890/iejg.594501

Abstract

References

  • [1] Ballico, E., Subsets of the variety X ⊂ Pn evincing the X-rank of a point of Pn, preprint.
  • [2] Ballico, E. and Bernardi, A., Decomposition of homogeneous polynomials with low rank, Math. Z. 271 (2012) 1141–1149.
  • [3] Bernardi, A., Gimigliano, A. and Idà, M., Computing symmetric rank for symmetric tensors, J. Symbolic. Comput. 46 (2011), no. 1, 34–53.
  • [4] Bernardi, A. and Ranestad, K., The cactus rank of cubic forms, J. Symbolic. Comput. 50 (2013) 291–297. DOI: 10.1016/j.jsc.2012.08.001
  • [5] Buczyn´ska, W. and Buczynśki, J., Secant varieties to high degree veronese reembeddings, catalecticant matrices and smoothable Gorenstein schemes. arXiv:1012.3562v4 [math.AG], J. Algebraic Geom. (to appear).
  • [6] Buczynśka, W. and Buczynśki, J., On the difference between the border rank and the smooth- able rank of a polynomial, arXiv:1305.1726.
  • [7] Buczynśki, J., Ginensky, A. and Landsberg, J. M., Determinantal equations for secant vari- eties and the Eisenbud-Koh-Stillman conjecture, J. London Math. Soc. (2) 88 (2013) 1–24.
  • [8] Buczynśki, J. and Landsberg, J. M., Ranks of tensors and a generalization of secant varieties, Linear Algebra Appl. 438 (2013), no. 2, 668–689.
  • [9] Comas, G., and Seiguer, M., On the rank of a binary form, Found. Comp. Math. 11 (2011), no. 1, 65–78.
  • [10] Hartshorne, R., Algebraic Geometry, Springer, Berlin, 1977.
  • [11] Iarrobino, A. and Kanev.,V., Power sums, Gorenstein algebras, and determinantal loci. Lec- ture Notes in Mathematics, vol. 1721, Springer-Verlag, Berlin, 1999, Appendix C by Iarrobino and Steven L. Kleiman.
  • [12] Landsberg, J. M., Tensors: Geometry and Applications, Graduate Studies in Mathematics, Vol. 128, Amer. Math. Soc. Providence, 2012.
Year 2014, , 126 - 132, 30.04.2014
https://doi.org/10.36890/iejg.594501

Abstract

References

  • [1] Ballico, E., Subsets of the variety X ⊂ Pn evincing the X-rank of a point of Pn, preprint.
  • [2] Ballico, E. and Bernardi, A., Decomposition of homogeneous polynomials with low rank, Math. Z. 271 (2012) 1141–1149.
  • [3] Bernardi, A., Gimigliano, A. and Idà, M., Computing symmetric rank for symmetric tensors, J. Symbolic. Comput. 46 (2011), no. 1, 34–53.
  • [4] Bernardi, A. and Ranestad, K., The cactus rank of cubic forms, J. Symbolic. Comput. 50 (2013) 291–297. DOI: 10.1016/j.jsc.2012.08.001
  • [5] Buczyn´ska, W. and Buczynśki, J., Secant varieties to high degree veronese reembeddings, catalecticant matrices and smoothable Gorenstein schemes. arXiv:1012.3562v4 [math.AG], J. Algebraic Geom. (to appear).
  • [6] Buczynśka, W. and Buczynśki, J., On the difference between the border rank and the smooth- able rank of a polynomial, arXiv:1305.1726.
  • [7] Buczynśki, J., Ginensky, A. and Landsberg, J. M., Determinantal equations for secant vari- eties and the Eisenbud-Koh-Stillman conjecture, J. London Math. Soc. (2) 88 (2013) 1–24.
  • [8] Buczynśki, J. and Landsberg, J. M., Ranks of tensors and a generalization of secant varieties, Linear Algebra Appl. 438 (2013), no. 2, 668–689.
  • [9] Comas, G., and Seiguer, M., On the rank of a binary form, Found. Comp. Math. 11 (2011), no. 1, 65–78.
  • [10] Hartshorne, R., Algebraic Geometry, Springer, Berlin, 1977.
  • [11] Iarrobino, A. and Kanev.,V., Power sums, Gorenstein algebras, and determinantal loci. Lec- ture Notes in Mathematics, vol. 1721, Springer-Verlag, Berlin, 1999, Appendix C by Iarrobino and Steven L. Kleiman.
  • [12] Landsberg, J. M., Tensors: Geometry and Applications, Graduate Studies in Mathematics, Vol. 128, Amer. Math. Soc. Providence, 2012.
There are 12 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Edoardo Ballıco This is me

Publication Date April 30, 2014
Published in Issue Year 2014

Cite

APA Ballıco, E. (2014). SYMMETRIC TENSOR RANK, CACTUS RANK AND RELATED COMPLEXITY MEASURES FOR HOMOGENEOUS POLYNOMIALS. International Electronic Journal of Geometry, 7(1), 126-132. https://doi.org/10.36890/iejg.594501
AMA Ballıco E. SYMMETRIC TENSOR RANK, CACTUS RANK AND RELATED COMPLEXITY MEASURES FOR HOMOGENEOUS POLYNOMIALS. Int. Electron. J. Geom. April 2014;7(1):126-132. doi:10.36890/iejg.594501
Chicago Ballıco, Edoardo. “SYMMETRIC TENSOR RANK, CACTUS RANK AND RELATED COMPLEXITY MEASURES FOR HOMOGENEOUS POLYNOMIALS”. International Electronic Journal of Geometry 7, no. 1 (April 2014): 126-32. https://doi.org/10.36890/iejg.594501.
EndNote Ballıco E (April 1, 2014) SYMMETRIC TENSOR RANK, CACTUS RANK AND RELATED COMPLEXITY MEASURES FOR HOMOGENEOUS POLYNOMIALS. International Electronic Journal of Geometry 7 1 126–132.
IEEE E. Ballıco, “SYMMETRIC TENSOR RANK, CACTUS RANK AND RELATED COMPLEXITY MEASURES FOR HOMOGENEOUS POLYNOMIALS”, Int. Electron. J. Geom., vol. 7, no. 1, pp. 126–132, 2014, doi: 10.36890/iejg.594501.
ISNAD Ballıco, Edoardo. “SYMMETRIC TENSOR RANK, CACTUS RANK AND RELATED COMPLEXITY MEASURES FOR HOMOGENEOUS POLYNOMIALS”. International Electronic Journal of Geometry 7/1 (April 2014), 126-132. https://doi.org/10.36890/iejg.594501.
JAMA Ballıco E. SYMMETRIC TENSOR RANK, CACTUS RANK AND RELATED COMPLEXITY MEASURES FOR HOMOGENEOUS POLYNOMIALS. Int. Electron. J. Geom. 2014;7:126–132.
MLA Ballıco, Edoardo. “SYMMETRIC TENSOR RANK, CACTUS RANK AND RELATED COMPLEXITY MEASURES FOR HOMOGENEOUS POLYNOMIALS”. International Electronic Journal of Geometry, vol. 7, no. 1, 2014, pp. 126-32, doi:10.36890/iejg.594501.
Vancouver Ballıco E. SYMMETRIC TENSOR RANK, CACTUS RANK AND RELATED COMPLEXITY MEASURES FOR HOMOGENEOUS POLYNOMIALS. Int. Electron. J. Geom. 2014;7(1):126-32.