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# About the Defectivity of Certain Segre--Veronese Varieties

Published:2008-10-01
Printed: Oct 2008
• Silvia Abrescia
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## Abstract

We study the regularity of the higher secant varieties of $\PP^1\times \PP^n$, embedded with divisors of type $(d,2)$ 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 $\PP^n$ is not Grassmann defective.
 Keywords: Waring problem, Segre--Veronese embedding, secant variety, Grassmann defectivity
 MSC Classifications: 14N15 - Classical problems, Schubert calculus 14N05 - Projective techniques [See also 51N35] 14M12 - Determinantal varieties [See also 13C40]

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