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2009 Secant Varieties of Segre-Veronese Varieties $\P^m \times \P^n$ Embedded by $\cO(1,2)$
Hirotachi Abo, Maria Chiara Brambilla
Experiment. Math. 18(3): 369-384 (2009).

Abstract

Let $X_{m,n}$ be the Segre-Veronese variety $\P^m \times \P^n$ embedded by the morphism given by $\cO(1,2)$. In this paper, we provide two functions $\underline{s}(m,n)\le \overline{s}(m,n)$ such that the $s$th secant variety of $X_{m,n}$ has the expected dimension if $s \leq \underline{s}(m,n)$ or $ \overline{s}(m,n) \leq s$. We also present a conjecturally complete list of defective secant varieties of such Segre-Veronese varieties.

Citation

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Hirotachi Abo. Maria Chiara Brambilla. "Secant Varieties of Segre-Veronese Varieties $\P^m \times \P^n$ Embedded by $\cO(1,2)$." Experiment. Math. 18 (3) 369 - 384, 2009.

Information

Published: 2009
First available in Project Euclid: 25 November 2009

zbMATH: 1198.14051
MathSciNet: MR2555705

Subjects:
Primary: 14M99 , 14Q99 , 15A69 , 15A72

Keywords: defectivity , secant varieties , Segre-Veronese varieties

Rights: Copyright © 2009 A K Peters, Ltd.

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Vol.18 • No. 3 • 2009
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