Higher secant varieties of $\mathbb P^n \times\mathbb P^ 1$ embedded in bi-degree $(a,b)$ - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Communications in Algebra Year : 2012

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

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.

Dates and versions

hal-00646167 , version 1 (28-11-2012)

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Cite

Edoardo Ballico, Alessandra Bernardi, Maria Virgina Catalisano. Higher secant varieties of $\mathbb P^n \times\mathbb P^ 1$ embedded in bi-degree $(a,b)$. Communications in Algebra, 2012, 40, 10, pp.3822-3840. ⟨10.1080/00927872.2011.595748⟩. ⟨hal-00646167⟩
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