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

2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (... - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
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.
Document type :
Journal articles
Domain :

https://hal.inria.fr/hal-00646167
Contributor : Alessandra Bernardi Connect in order to contact the contributor
Submitted on : Wednesday, November 28, 2012 - 10:30:55 AM
Last modification on : Monday, October 12, 2020 - 10:27:38 AM

### Citation

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, Taylor & Francis, 2012, 40, pp.3822-3840. ⟨10.1080/00927872.2011.595748⟩. ⟨hal-00646167⟩

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