IJPAM: Volume 66, No. 4 (2011)

ON THE $X$-RANKS OF POINTS ON $\mathbb {P}^n$ ( $X\subset \mathbb {P}^n$ A CURVE),
THE TANGENT DEVELOPABLE OF $X$, AND
THE UNIQUENESS OF SETS $S\subset X$ COMPUTING $X$-RANKS

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


Abstract.Let $X\subset \mathbb {P}^n$, $n \ge 4$, be an integral projective curve. Let $\tau (X)\subset \mathbb {P}^n$ be the tangent developable of $X$. For each $P\in \mathbb {P}^n$ let $r_X(P)$ be the minimal cardinality of a set $S\subset X$ spanning $X$ and $\mathcal {S}(X,P)$ the set of all $S\subset X$ computing $r_X(P)$. Here we give many cases with $\sharp (\mathcal {S}(X,P))=1$ and show that if $X$ is smooth, then $r_X(P)\ge 3$ for a general $P\in \tau (X)$.

Received: October 11, 2010

AMS Subject Classification: 14N05

Key Words and Phrases: ranks, secant variety, tangent developable, tangential projection

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 4