In this paper we compute the dimension of all the s-th higher secant varieties of the Segre-Veronese embeddings Yd of the product P1 x P1 x P1 in the projective Space P^N via divisors of multi-degree 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) ard s = 2h + 1, with defect 1 in both cases.
Segre-Veronese embeddings of P^1xP^1xP^1 and their secant varieties
CATALISANO, MARIA VIRGINIA;GERAMITA, ANTHONY VITO;
2007-01-01
Abstract
In this paper we compute the dimension of all the s-th higher secant varieties of the Segre-Veronese embeddings Yd of the product P1 x P1 x P1 in the projective Space P^N via divisors of multi-degree 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) ard s = 2h + 1, with defect 1 in both cases.
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