IJPAM: Volume 93, No. 6 (2014)
RANK OF TRIVARIATE POLYNOMIALS; A LOCAL
UNIQUENESS FOR MULTIVARIATE POLYNOMIALS
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
Abstract. For all integers and and . Let , , be the Veronese embedding. We discuss the uniqueness (only for trivariate polynomials) and the local uniqueness of a decomposition of a polynomial into powers of linear forms in the following sense. Take . Let be the set of all such that , (where is the linear span), and for any . We prove that (resp. is a isolated point of ) if , and has the general uniform position (resp. and has general postulation). We do the same for zero-dimensional schemes (scheme rank or cactus rank).
Received: March 1, 2014
AMS Subject Classification: 14N05
Key Words and Phrases: symmetric tensor rank, trivariate polynomial, zero-dimensional scheme, multivariate polynomial
Download paper from here.
DOI: 10.12732/ijpam.v93i6.7 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 807 - 812
This work is licensed under the Creative Commons Attribution International License (CC BY).