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

Ballico, Edoardo ; Bernardi, Alessandra ; Catalisano, M. Virginia (2011) Higher secant varieties of $\mathbb P^n \times\mathbb P^ 1$ embedded in bi-degree $(a,b)$. [Preprint]
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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.

Abstract
Document type
Preprint
Creators
CreatorsAffiliationORCID
Ballico, Edoardo
Bernardi, Alessandra
Catalisano, M. Virginia
Subjects
DOI
Deposit date
07 Mar 2011 10:53