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, A.; Carlini, E.; Catalisano, M. V.; Gimigliano, A.; Oneto, A.. - In: MATHEMATICS. - ISSN 2227-7390. - ELETTRONICO. - 6:12(2018), pp. 314-399. [10.3390/math6120314]

The Hitchhiker guide to: Secant varieties and tensor decomposition

Carlini E.;
2018

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2781459