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About the Defectivity of Certain Segre–Veronese Varieties

Published online by Cambridge University Press:  20 November 2018

Silvia Abrescia
Silvia Abrescia*
Affiliation:
Dipartimento di Matematica, Università di Bologna, 40137 Bologna, Italy e-mail:abrescia@dm.unibo.it
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Abstract

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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.

Keywords

14N1514N0514M12Waring problemSegre–Veronese embeddingsecant varietyGrassmann defectivity
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 5 , October 2008 , pp. 961 - 974
Copyright
Copyright © Canadian Mathematical Society 2008

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