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 which 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.
|Titolo:||The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition|
|Data di pubblicazione:||2018|
|Appare nelle tipologie:||01.01 - Articolo su rivista|