HOMOGENEOUS POLYNOMIALS WITH TWO SETS COMPUTING THEIR SYMMETRIC TENSOR RANK

E. Ballico

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: ballico@science.unitn.it

Abstract. Let $x_{m,d} \subset \mathbb {P}^{\binom{m+d}{m}-1}$ be the order Veronese embedding of $\mathbb {P}^m$ . Here we classify points $p\in \mathbb {P}^{\binom{m+d}{m}-1}$ with symmetric rank and whose symmetric rank is computed by at least sets $A, B\subset \mathbb {P}^m$ such that no 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 $X_{m,d}$ .