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.
Edoardo Ballico, Alessandra Bernardi, Maria Virginia Catalisano (2012). Higher Secant Varieties of ℙn × ℙ1Embedded in Bi-Degree (a,b). COMMUNICATIONS IN ALGEBRA, 40, 3822-3840 [10.1080/00927872.2011.595748].
Higher Secant Varieties of ℙn × ℙ1Embedded in Bi-Degree (a,b)
BERNARDI, ALESSANDRA;
2012
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.File in questo prodotto:
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