IJPAM: Volume 81, No. 6 (2012)

ON THE CONNECTED RANK FOR PROJECTIVE VARIETIES

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract. We start the discussion of the following query. Let $X\subset \mathbb {P}^n$ be an integral and non-degenerate curve. For each $P\in \mathbb {P}^n$ let $r_{X,s}(P)$ (resp. $r_{X,c}(P)$, resp. $r_{X,cc}(P)$) be the minimal degree of a zero-dimensional (resp. zero-dimensional and connected, resp. zero-dimensional connected and curvilinear) scheme $Z$ such that $P\in \langle Z\rangle$, where $\langle \ \ \rangle$ denote the linear span. Compute the maximal integer $r_{X,s}(P)$ and $r_{X,c}(P)$ when $P$ is arbitrary (resp. general) in $\mathbb {P}^n$.

Received: October 14, 2012

AMS Subject Classification: 14N10, 14H45

Key Words and Phrases: symmetric tensor rank, connected rank, curvilinear scheme, cactus rank

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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: 81
Issue: 6