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.
The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition / Bernardi, Alessandra; Carlini, Enrico; Virginia Catalisano, Maria; Gimigliano, Alessandro; Oneto, Alessandro. - In: MATHEMATICS. - ISSN 2227-7390. - 6:12(2018), pp. 31401-31486. [10.3390/math6120314]
Titolo: | The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition | |
Autori: | Bernardi, Alessandra; Carlini, Enrico; Virginia Catalisano, Maria; Gimigliano, Alessandro; Oneto, Alessandro | |
Autori Unitn: | ||
Titolo del periodico: | MATHEMATICS | |
Anno di pubblicazione: | 2018 | |
Numero e parte del fascicolo: | 12 | |
Codice identificativo Scopus: | 2-s2.0-85059465353 | |
Codice identificativo WOS: | WOS:000454519300042 | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.3390/math6120314 | |
Handle: | http://hdl.handle.net/11572/220897 | |
Citazione: | The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition / Bernardi, Alessandra; Carlini, Enrico; Virginia Catalisano, Maria; Gimigliano, Alessandro; Oneto, Alessandro. - In: MATHEMATICS. - ISSN 2227-7390. - 6:12(2018), pp. 31401-31486. [10.3390/math6120314] | |
Appare nelle tipologie: | 03.1 Articolo su rivista (Journal article) |
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