About the Defectivity of Certain Segre–Veronese Varieties

Abrescia, Silvia

Canadian journal of mathematics, Tome 60 (2008) no. 5, pp. 961-974

Résumé

We study the regularity of the higher secant varieties of ${{\mathbb{P}}^{1}}\times {{\mathbb{P}}^{n}}$ , embedded with divisors of type $\text{(}d\text{,}\,\text{2)}$ and $(d,3)$ . We produce, for the highest defective cases, a “determinantal” equation of the secant variety. As a corollary, we prove that the Veronese triple embedding of ${{\mathbb{P}}^{n}}$ is not Grassmann defective.

Détail

DOI : 10.4153/CJM-2008-042-7

Mots-clés : 14N15, 14N05, 14M12, Waring problem, Segre–Veronese embedding, secant variety, Grassmann defectivity

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