Projective surfaces with bi-elliptic hyperplane sections.
Segre-Veronese embeddings of P x P x P and their secant varieties.
In this paper we compute the dimension of all the s higher secant varieties of the Segre-Veronese embeddings Y of the product P × P × P in the projective space P via divisors of multidegree d = (a,b,c) (N = (a+1)(b+1)(c+1) - 1). We find that Y 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.
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