# 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: ballico@science.unitn.it

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.