IJPAM: Volume 96, No. 1 (2014)

ON THE STRATIFICATION OF THE PROJECTIVE SPACE
BY THE $X$-RANK FOR A CERTAIN CONFIGURATION
$X$ OF RATIONAL NORMAL CURVES

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


Abstract. Let $\nu _d: \mathbb {P}^m \to \mathbb {P}^N$, $m\ge 2$, $N:=\binom{m+d}{m}-1$, denote the Veronese embedding. Fix $O\in \mathbb {P}^m$ and let $T_m$ be the union of $m$ lines of $\mathbb {P}^m$ passing through $O$ and with $\langle T_m\rangle =\mathbb {P}^m$, where $\langle \ \rangle$ denote the linear span ($T_m$ is an angle or a coordinate frame). Set $T_{m,d}:= \nu _d(T_m)$. In this note we study the stratification by $T_{m,d}$-rank of $\langle T_{m,d}\rangle$. We give a sharp upper bound for this rank, prove a concision result (in a precise quantitative way) and study some cases with high rank.

Received: July 8, 2014

AMS Subject Classification: 14N05

Key Words and Phrases: symmetric tensor rank, reducible curve, border rank, rational normal curve

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DOI: 10.12732/ijpam.v96i1.8 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: 96
Issue: 1
Pages: 105 - 115


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