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About the Defectivity of Certain Segre--Veronese Varieties |
Canad. J. Math. 60(2008), 961-974
Published:2008-10-01
Printed: Oct 2008
Printed: Oct 2008
- Silvia Abrescia
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] |