IJPAM: Volume 60, No. 1 (2010)

A PROJECTIVE CURVE $X\subset \mathbb {P}^n$

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

Abstract.Let $X\subset \mathbb {P}^n$, $n\ge 3$, be an integral and non-degenerate curve For any $P\in \mathbb {P}^n$ let $r_X(P)$ be the minimal cardinality of a set $S\subset X$ such that $P\in \langle S\rangle$. Set $F_X(k):= \{P\in \mathbb {P}^n: r_X(P)\ge k\}$. Here we prove that $F_X(k)$ contains no linear $(n-k+1)$-dimensional subspace and no $(n-k+2)$-dimensional complete subvariety.

Received: January 14, 2010

AMS Subject Classification: 14N05, 14H50

Key Words and Phrases: rank, linear span, non-degenerate curve

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 1