Higher secant varieties of $\mathbb P^n \times\mathbb P^ 1$ embedded in bi-degree $(a,b)$

Details Higher secant varieties of $\mathbb P^n \times\mathbb P^ 1$ embedded in bi-degree $(a,b)$ Higher secant varieties of $\mathbb P^n \times\mathbb P^ 1$ embedded in bi-degree $(a,b)$

2011-03-06

arxiv.org/abs/1103.1151v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

In this paper we compute the dimension of all the higher secant varieties to
the Segre-Veronese embedding of $\mathbb{P}^n\times \mathbb{P}^1$ via the
section of the sheaf $\mathcal{O}(a,b)$ for any $n,a,b\in \mathbb{Z}^+$. We
relate this result to the Grassmann Defectivity of Veronese varieties and we
classify all the Grassmann $(1,s-1)$-defective Veronese varieties.

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