Higher Secant Varieties of n × 1 Embedded in Bi-Degree ( a , b )

Author: Ballico Edoardo  

Publisher: Taylor & Francis Ltd

ISSN: 0092-7872

Source: Communications in Algebra, Vol.40, Iss.10, 2012-10, pp. : 3822-3840

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Abstract

In this article, we compute the dimension of all the higher secant varieties to the Segre-Veronese embedding of n × 1 via the section of the sheaf (a, b) for any n, a, b ∈ +. We relate this result to the Grassmann Defectivity of Veronese varieties and we classify all the Grassmann (1, s − 1)-defective Veronese varieties.