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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 Waring problem, Segre--Veronese embedding, secant variety, Grassmann defectivity
MSC Classifications: 14N15, 14N05, 14M12 show english descriptions Classical problems, Schubert calculus
Projective techniques [See also 51N35]
Determinantal varieties [See also 13C40]
14N15 - Classical problems, Schubert calculus
14N05 - Projective techniques [See also 51N35]
14M12 - Determinantal varieties [See also 13C40]
 

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