IJPAM: Volume 67, No. 2 (2011)

HOMOGENEOUS POLYNOMIALS WITH TWO SETS
COMPUTING THEIR SYMMETRIC TENSOR RANK

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract. Let $x_{m,d} \subset \mathbb {P}^{\binom{m+d}{m}-1}$ be the order $d$ Veronese embedding of $\mathbb {P}^m$. Here we classify points $p\in \mathbb {P}^{\binom{m+d}{m}-1}$ with symmetric rank $d+1$ and whose symmetric rank is computed by at least $2$ sets $A, B\subset \mathbb {P}^m$ such that no $3$ of the points of $A\cup B$ are collinear. In these cases the symmetric rank is computed by an infinite (and one-dimensional) family of subsets of $X_{m,d}$.



Received: August 8, 2010

AMS Subject Classification: 14N05

Key Words and Phrases: rsymmetric tensor rank, Veronese variety

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 67
Issue: 2