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

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

Öz

Kaynakça

  • [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.
Yıl 2014, , 126 - 132, 30.04.2014
https://doi.org/10.36890/iejg.594501

Öz

Kaynakça

  • [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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Edoardo Ballıco Bu kişi benim

Yayımlanma Tarihi 30 Nisan 2014
Yayımlandığı Sayı Yıl 2014

Kaynak Göster

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. Nisan 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, sy. 1 (Nisan 2014): 126-32. https://doi.org/10.36890/iejg.594501.
EndNote Ballıco E (01 Nisan 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., c. 7, sy. 1, ss. 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 (Nisan 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, c. 7, sy. 1, 2014, ss. 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.