In this paper we compute the dimension of all the higher secant varieties to the Segre-Veronese embedding of P^n x P^1 via the section of the shea O(a,b) for any n,a,b natural numbers. 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 P^n x P^1 embedded in bi-degree (a,b)
CATALISANO, MARIA VIRGINIA
2012-01-01
Abstract
In this paper we compute the dimension of all the higher secant varieties to the Segre-Veronese embedding of P^n x P^1 via the section of the shea O(a,b) for any n,a,b natural numbers. We relate this result to the Grassmann defectivity of Veronese varieties and we classify all the Grassmann (1,s-1)-defective Veronese varieties.
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