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

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 $s\le \underline{s}(m,n)$ or $\bar{s}(m,n)\le s$. We also present a conjecturally complete list of defective secant varieties of such Segre-Veronese varieties.

18 pages; published version; corrected typo in Definition 4.3

References in corpus (2)

• Markov basis and Groebner basis of Segre-Veronese configuration for testing independence in group-wise selections
• Shell-mediated tunnelling between (anti-)de Sitter vacua

Cited by in corpus (1)

• A syzygetic approach to the smoothability of zero-dimensional schemes