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arXiv · 0809.4837

Secant varieties of Segre-Veronese varieties P^m x P^n embedded by O(1,2)

Hirotachi Abo·Maria Chiara Brambilla
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Abstract

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

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Hirotachi Abo, Maria Chiara Brambilla. 2012-02-06. Secant varieties of Segre-Veronese varieties P^m x P^n embedded by O(1,2). https://arxiv.org/abs/0809.4837

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