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arXiv · 1812.10267

The Hitchhiker guide to: Secant Varieties and Tensor Decomposition

Alessandra Bernardi·Enrico Carlini·Maria Virginia Catalisano·Alessandro Gimigliano·Alessandro Oneto
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Abstract

We consider here the problem, which is quite classical in Algebraic geometry, of studying the secant varieties of a projective variety $X$. The case we concentrate on is when $X$ is a Veronese variety, a Grassmannian or a Segre variety. Not only these varieties are among the ones that have been most classically studied, but a strong motivation in taking them into consideration is the fact that they parameterize, respectively, symmetric, skew-symmetric and general tensors, which are decomposable, and their secant varieties give a stratification of tensors via tensor rank. We collect here most of the known results and the open problems on this fascinating subject.

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Alessandra Bernardi, Enrico Carlini, Maria Virginia Catalisano, Alessandro Gimigliano, Alessandro Oneto. 2018-12-26. The Hitchhiker guide to: Secant Varieties and Tensor Decomposition. https://doi.org/10.3390/math6120314

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