Secant Varieties of (P ^1) X .... X (P ^1) (n-times) are NOT Defective for n \geq 5

Abstract

Let V_n be the Segre embedding of (P^1) x ... X (P^1) (n times). We prove that the higher secant varieties, \sigma_s(V_n), always have the expected dimension, except for \sigma_3(V_4), which is of dimension 1 less than expected.