Higher secant varieties of Segre-Veronese varieties

Details Higher secant varieties of Segre-Veronese varieties Higher secant varieties of Segre-Veronese varieties

2003-09-24

arxiv.org/abs/math/0309399v1

Mathematics

Algebraic Geometry

12 pages, plain TEX

Scientific paper

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.

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