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About the Defectivity of Certain Segre–Veronese Varieties
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- Journal:
- Canadian Journal of Mathematics / Volume 60 / Issue 5 / October 2008
- Published online by Cambridge University Press:
- 20 November 2018, pp. 961-974
- Print publication:
- October 2008
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- Article
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- You have access
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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.
