Resumen de Segre-Veronese embeddings of P1 × P1 × P1 and their secant varieties

Maria Virginia Catalisano, Anthony V. Geramita, A. Gimigliano

• In this paper we compute the dimension of all the sth higher secant varieties of the SegreVeronese 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