TY  - JOUR
T1  - SYMMETRIC TENSOR RANK, CACTUS RANK AND RELATED COMPLEXITY MEASURES FOR HOMOGENEOUS POLYNOMIALS
AU  - Ballıco, Edoardo
PY  - 2014
DA  - April
DO  - 10.36890/iejg.594501
JF  - International Electronic Journal of Geometry
JO  - Int. Electron. J. Geom.
PB  - Kazım İlarslan
WT  - DergiPark
SN  - 1307-5624
SP  - 126
EP  - 132
VL  - 7
IS  - 1
LA  - en
KW  - symmetric tensor rank
KW  - cactus rank
KW  - complexity rank
CR  - [1] Ballico, E., Subsets of the variety X ⊂ Pn evincing the X-rank of a point of Pn, preprint.
CR  - [2]  Ballico,  E. and Bernardi, A.,  Decomposition of homogeneous polynomials with low rank, Math. 
Z. 271 (2012) 1141–1149.
CR  - [3]  Bernardi, A., Gimigliano, A. and Idà, M., Computing symmetric rank for symmetric tensors, J. 
Symbolic. Comput. 46 (2011), no. 1, 34–53.
CR  - [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
CR  - [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).
CR  - [6] Buczynśka, W. and Buczynśki, J., On the difference between the border rank and the smooth- 
able rank of a polynomial, arXiv:1305.1726.
CR  - [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.
CR  - [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.
CR  - [9] Comas, G., and Seiguer, M., On the rank of a binary form, Found. Comp. Math. 11 (2011), no. 1, 
65–78.
CR  - [10] Hartshorne, R., Algebraic Geometry, Springer, Berlin, 1977.
CR  - [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.
CR  - [12] Landsberg, J. M., Tensors: Geometry and Applications, Graduate Studies in Mathematics,
Vol. 128, Amer. Math. Soc. Providence, 2012.
UR  - https://doi.org/10.36890/iejg.594501
L1  - https://dergipark.org.tr/en/download/article-file/766120
ER  -