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arXiv · 1103.1151

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

Edoardo Ballico·Alessandra Bernardi·Maria Virginia Catalisano
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Abstract

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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Edoardo Ballico, Alessandra Bernardi, Maria Virginia Catalisano. 2011-03-06. Higher secant varieties of $\mathbb P^n \times\mathbb P^ 1$ embedded in bi-degree $(a,b)$. https://doi.org/10.1080/00927872.2011.595748

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