# IJPAM: Volume 65, No. 1 (2010)

A FINITENESS RESULT ON THE SETS
COMPUTING -RANK AND SPANNING
A PRESCRIBED LINEAR SPACE

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

Abstract.Let be an integral and non-degenerate variety defined over an algebraically closed field such that . For each the -rank of is the minimal cardinality of a set such that . Let denote the set of all subsets such that and . Let the subset of the Grassmannian parametrizing all linear spaces , . For each set . Here we prove that every is finite.

Received: September 23, 2010

AMS Subject Classification: 14N05

Key Words and Phrases: -rank, symmetric tensor rank

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 65
Issue: 1