Experimental Mathematics

Secant Varieties of Segre-Veronese Varieties $\P^m \times \P^n$ Embedded by $\cO(1,2)$

Hirotachi Abo and Maria Chiara Brambilla

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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.

Article information

Source
Experiment. Math., Volume 18, Issue 3 (2009), 369-384.

Dates
First available in Project Euclid: 25 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.em/1259158472

Mathematical Reviews number (MathSciNet)
MR2555705

Zentralblatt MATH identifier
1198.14051

Subjects
Primary: 14M99: None of the above, but in this section 14Q99: None of the above, but in this section 15A69: Multilinear algebra, tensor products 15A72: Vector and tensor algebra, theory of invariants [See also 13A50, 14L24]

Keywords
Secant varieties Segre-Veronese varieties defectivity

Citation

Abo, Hirotachi; Brambilla, Maria Chiara. Secant Varieties of Segre-Veronese Varieties $\P^m \times \P^n$ Embedded by $\cO(1,2)$. Experiment. Math. 18 (2009), no. 3, 369--384. https://projecteuclid.org/euclid.em/1259158472


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