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.
The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition
MARIA V. CATALISANO;
2018-01-01
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 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.File | Dimensione | Formato | |
---|---|---|---|
mathematics-06-00314-v2.pdf
accesso aperto
Tipologia:
Documento in versione editoriale
Dimensione
893.76 kB
Formato
Adobe PDF
|
893.76 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.