IJPAM: Volume 78, No. 2 (2012)

SYMMETRIC TENSOR RANK OF POINTS
IN THE LINEAR SPAN OF SUITABLE
ZERO-DIMENSIONAL SUBSCHEMES

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract. Let $\nu _d: \mathbb {P}^m\to \mathbb {P}^n$ the $d$-Veronese embedding. Fix $P\in \mathbb {P}^n$ such that $P\in \langle \nu _d(Z)\rangle$ with $Z$ in linearly general position (or in $t$-uniform position). Here we give lower bounds on the symmetric rank of $P$ in terms of $\deg (Z)$.

Received: February 27, 2012

AMS Subject Classification: 14N05

Key Words and Phrases: symmetric tensor rank, cactus rank, zero-dimensional scheme

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 2