IJPAM: Volume 58, No. 2 (2010)

ON SOME VARIATIONS OF THE NOTION OF RANKS
(WITH PRESCRIBED POINTS) OF A VARIETY $X \subset \mathbb {P}^n$

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


Abstract.Let $X \subset \mathbb {P}^n$, be a integral variety. For each finite $B\subset X$ we study the rank function $r_{X; B}: \mathbb {P}^n \to \mathbb {Z}$ (resp. $\rho _{X;B}$): for any $P\in \mathbb {P}^n$ the rank $r_{X;B}(P)$ is the minimal cardinality of a set $S\subset X$ such that $P\in \langle S\rangle$ and either $B \subseteq S$ or $S\subseteq B$ (resp. $P \in \langle S\cup B\rangle$ and no condition on $S\cap B$). Here we describes the extremal cases when $\dim (X)=1$ and $\sharp (B)=1$.

Received: December 11, 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: 58
Issue: 2