Linearly dependent subsets of Segre varieties.

We study the linear algebra of finite subsets S of a Segre variety X. In particular we classify the pairs (S, X) with S linear dependent and # (S) ≤ 5 . We consider an additional condition for linear dependent sets, i.e. that no two of their points are contained in a line of X, and get far better lower bounds for # (S) in term of the dimension and number of the factors of X. In this discussion and in the classification of the case # (S) = 5 , X ≅ P 1 × P 1 × P 1 we use the rational normal curves contained in X. [ABSTRACT FROM AUTHOR]