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.
Higher Secant Varieties of ℙn × ℙ1Embedded in Bi-Degree (a,b) / Edoardo Ballico; Alessandra Bernardi; Maria Virginia Catalisano. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - STAMPA. - 40:(2012), pp. 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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