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 $X$.
Edoardo Ballico, Alessandra Bernardi, Maria Virginia Catalisano, Luca Chiantini (2013). Grassmann secants, identifiability, and linear systems of tensors. LINEAR ALGEBRA AND ITS APPLICATIONS, 438, 121-135 [10.1016/j.laa.2012.07.045].
Grassmann secants, identifiability, and linear systems of tensors
BERNARDI, ALESSANDRA;
2013
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 $X$.File in questo prodotto:
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