IJPAM: Volume 66, No. 4 (2011)

SUBSETS OF A 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.Fix integers $k \ge 2$ and $n \ge 2k-1$. Fix a $(k-2)$-dimensional linear subspace $V \subset \mathbb {P}^n$. Here we construct smooth curves $X\subset \mathbb {P}^n$ such that for a general $P\in V$ there is $S\subset X$ computing the $X$-rank of $P$ and containing $V$. For fixed $X$ and $V$ we also get infinitely many such sets $S$.

Received: August 17, 2010

AMS Subject Classification: 14N05

Key Words and Phrases: $X$-rank

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