Grassmann secants and linear systems of tensors

Ballico, Edoardo ; Bernardi, Alessandra ; Catalisano, Maria Virgina ; Chiantini, Luca (2011) Grassmann secants and linear systems of tensors. [Preprint]

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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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