On the identifiability of binary Segre products

Abstract

We prove that a product of m > 5 m>5 copies of P 1 \mathbb {P}^1 , embedded in the projective space P r \mathbb {P}^r by the standard Segre embedding, is k k -identifiable (i.e. a general point of the secant variety S k ( X ) S^k(X) is contained in only one ( k + 1 ) (k+1) -secant k k -space), for all k k such that k + 1 ≤ 2 m − 1 / m k+1\leq 2^{m-1}/m .