The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition

Alessandra Bernardi, Enrico Carlini, Maria Catalisano, Alessandro Gimigliano, Alessandro Oneto
2018 Mathematics  
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,
more » ... 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.
doi:10.3390/math6120314 fatcat:5ayrmnulincb7fke7xce3eunsi