M. V. Catalisano, A. V. Geramita, A. Gimigliano
Published 2003-09-24Version 1
We study the dimension of the higher secant varieties $X^s$ of ${\Bbb X} = {\Bbb P}^{n_1}\times ...\times {\Bbb P}^{n_t}$ embedded the morphism given by ${\cal O}_{\Bbb X}({a_1,...,a_t})$. We call it a {\it Segre-Veronese variety} and the embedding a {\it Segre-Veronese embedding}. In several cases (e.g. for 3 factors {\Bbb P}^{1}, or when $s$ is small) we show that $X^s$ has the expected dimension except for a few cases. A list of examples of defective $X^s$'s is given.
Comments: 12 pages, plain TEX
Secant Varieties of (P ^1) X .... X (P ^1) (n-times) are NOT Defective for n \geq 5
Higher secant varieties of $\mathbb{P}^n \times \mathbb{P}^m$ embedded in bi-degree $(1,d)$
Secant varieties of Segre-Veronese varieties P^m x P^n embedded by O(1,2)
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