IJPAM: Volume 70, No. 5 (2011)

WHEN A FINITE SUBSET $S\subset X\subset \mathbb {P}^n$
COMPUTES THE $X$-RANK OF SOME $P\in \mathbb {P}^n$?

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 an integral and projective variety. For any $P\in \mathbb {P}^n$ the $X$-rank of $P$ is the minimal cardinality of a set $S\subset X$ such that $P\in \langle S\rangle$; any such $S$ with minimal cardinality is said to compute the $X$-rank of $P$. Fix $S\subset X$. Here we give onditions on $X$ and $S$ which imply the existence of $P\in \mathbb {P}^n$ such that $S$ compute the $X$-rank of $P$.

Received: March 12, 2011

AMS Subject Classification: 14N05

Key Words and Phrases: $X$-rank

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 5