IJPAM: Volume 62, No. 1 (2010)

AN $X$-RANK CHARACTERIZATION OF
RATIONAL NORMAL CURVES

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


Abstract.Here we characterize the rational normal curves of $\mathbb {P}^n$, $n \ge 5$ and odd, among the smooth curves $X \subset \mathbb {P}^n$ in terms of the dimension of all $P\in \mathbb {P}^n$ with $X$-rank $\ge (n+3)/2$ and with $X$-border rank maximal, $(n+1)/2$. We also prove that this set is large if $X$ is a linearly normal elliptic curve.

Received: March 16, 2010

AMS Subject Classification: 14H50, 14N05

Key Words and Phrases: ranks, border rank, rational normal curve, elliptic linearly normal curve

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 62
Issue: 1