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

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

2008-09-28

arxiv.org/abs/0809.4837v3

Experimental Mathematics, 18 (2009) 3, 369-384

Mathematics

Algebraic Geometry

18 pages; published version; corrected typo in Definition 4.3

Scientific paper

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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