Grassmann secants and linear systems of tensors

Abstract : For any irreducible non-degenerate variety $X \subset \mathbb{P}^r$ , we relate the dimension of the $s$-th secant varieties of the Segre embedding of $\mathbb{P}^k\times X$ to the dimension of the $(k,s)$-Grassmann secant variety $GS_X(k,s)$ of $X$. We also give a criterion for the $s$-identifiability of $X$.
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Edoardo Ballico, Alessandra Bernardi, Maria Virgina Catalisano, Luca Chiantini. Grassmann secants and linear systems of tensors. Linear Algebra and its Applications, Elsevier, 2013, 438, pp.121-135. ⟨http://www.sciencedirect.com/science/article/pii/S0024379512006076⟩. ⟨10.1016/j.laa.2012.07.045⟩. ⟨inria-00637780⟩

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