IJPAM: Volume 61, No. 1 (2010)

ON THE RANKS OF A RATIONAL NORMAL CURVE
OF $\mathbb {P}^n$ MINUS OR PLUS FINITELY MANY POINTS

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


Abstract.Let $X \subset \mathbb {P}^n$, be a rational normal curve. For each finite $B\subset X$ and $D\subset \mathbb {P}^n\backslash X$ we study the rank function $r_{(X\backslash B)\cup D}: \mathbb {P}^n \to \mathbb {Z}$: for any $P\in \mathbb {P}^n$ the rank $r_{(X\backslash B)\cup D}(P)$ is the minimal cardinality of a set $S\subset (X\backslash B)\cup D$ such that $P\in \langle S\rangle$.

Received: December 3, 2009

AMS Subject Classification: 14N05, 14H99

Key Words and Phrases: rational normal curve, secant varieties, linear span

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 61
Issue: 1