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.
@article{urn:eudml:doc:41792,
title = {Segre-Veronese embeddings of P1 x P1 x P1 and their secant varieties.},
journal = {Collectanea Mathematica},
volume = {58},
year = {2007},
pages = {1-24},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41792}
}
Catalisano, Maria Virginia; Geramita, Anthony V.; Gimigliano, Alessandro. Segre-Veronese embeddings of P1 x P1 x P1 and their secant varieties.. Collectanea Mathematica, Tome 58 (2007) pp. 1-24. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41792/