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

Edoardo Ballıco

doi:10.36890/iejg.594501

Research Article

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

Year 2014, Volume: 7 Issue: 1, 126 - 132, 30.04.2014

Edoardo Ballıco

https://doi.org/10.36890/iejg.594501

Abstract

Keywords

symmetric tensor rank, cactus rank, complexity rank

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, Volume: 7 Issue: 1, 126 - 132, 30.04.2014

Edoardo Ballıco

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 Volume: 7 Issue: 1

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.