Segre-Veronese embeddings of P1 x P1 x P1 and their secant varieties.
In this paper we compute the dimension of all the sth higher secant varieties of the Segre-Veronese embeddings Yd of the product P1 × P1 × P1 in the projective space PN via divisors of multidegree d = (a,b,c) (N = (a+1)(b+1)(c+1) - 1). We find that Yd has no deficient higher secant varieties, unless d = (2,2,2) and s = 7, or d = (2h,1,1) and s = 2h + 1, with defect 1 in both cases.