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, σ_s(V_n), always have the expected dimension, except for σ_3(V_4), which is of dimension 1 less than expected.

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