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

**A FINITENESS RESULT ON THE SETS**

COMPUTING -RANK AND SPANNING

A PRESCRIBED LINEAR SPACE

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]

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