IJPAM: Volume 95, No. 4 (2014)

SYMMETRIC TENSOR RANK
WITH RESPECT TO CURVES

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY


Abstract. Let $\nu :d: \mathbb {P}^m\to \mathbb {P}^r$, $r:= \binom{m+d}{m}-1$, be the order $d$ Veronese embedding. For any $P\in \mathbb {P}^r$ let $c( P)$ (resp. $cc( P)$, resp. $ic( P)$) be the minimal degree of a reduced (resp. reduced and connected, resp. integral) curve $C\subset \mathbb {P}^m$ such that $P\in \langle \nu _d( C)\rangle$. We study these invariants when $P$ has border rank $\le 4$.

Received: August 1, 2014

AMS Subject Classification: 14N05

Key Words and Phrases: symmetric tensor rank, irreducible curve, border rank

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DOI: 10.12732/ijpam.v95i4.16 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 95
Issue: 4
Pages: 629 - 634


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