IJPAM: Volume 65, No. 2 (2010)

A CONJECTURE ON THE RANK OF NON-GENERAL
POINTS OF SECANT VARIETIES OF VERONESE
EMBEDDINGS OF PROJECTIVE SPACES

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 $d$ Veronese embedding of $\mathbb {P}^m$. Here we conjecture that for certain secant varieties $\sigma _t(X_{m,d})$ a hypersurface of it has points of symmetric tensor rank $>t$. We look at the corresponding conjecture for curves.

Received: September 23, 2010

AMS Subject Classification: 14N05

Key Words and Phrases: symmetric tensor rank, Veronese variety, $X$-rank, Veronese embedding

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 65
Issue: 2