Skip to main content
Article thumbnail
Location of Repository

Reviewed by Enrico Carlini References

By J. M. [l, Joseph M. (-txam) Teitler, J. Alex, A. Hirschowitz and J. Algebr Geom

Abstract

On the ranks and border ranks of symmetric tensors. (English summary) Found. Comput. Math. 10 (2010), no. 3, 339–366.1615-3383 This paper deals with sums of powers decompositions of homogenous polynomials. The authors study two quantities related to a degree d form F. The rank (also called Waring rank in this paper) R(F) represents the minimal number of linear forms xi such that one has F = ∑R(F) 1 xd i. The border rank R(F) represents the minimal number such that F is in the Zariski closure of forms of rank R(F). Thus, for example, R(x2y) = 3 and R(x2y) = 2. Among the many results in the paper, the authors compute R for special monomials. They also produce a lower bound for R(F), F any form, depending on the singularities of the hypersurface F = 0. Explicit lower bounds are presented for the determinant and the permanent polynomials. Finally, they present an upper bound for R(F), for any form F

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.2734
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.