scholarly journals On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry

2021 ◽  
Vol 76 (1) ◽  
pp. 29-89
Author(s):  
S Ballet ◽  
J Pieltant ◽  
M Rambaud ◽  
H Randriambololona ◽  
R Rolland ◽  
...  
Keyword(s):  
Algebraic Geometry ◽  
Finite Fields ◽  
Tensor Rank

scholarly journals The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 314 ◽  
Author(s):  
Alessandra Bernardi ◽  
Enrico Carlini ◽  
Maria Catalisano ◽  
Alessandro Gimigliano ◽  
Alessandro Oneto
Keyword(s):  
Algebraic Geometry ◽  
Projective Variety ◽  
Tensor Decomposition ◽  
Tensor Rank ◽  
Segre Variety ◽  
Secant Varieties ◽  
Open Problems ◽  
Veronese Variety ◽  
Strong Motivation

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.

scholarly journals On the tensor rank of the multiplication in the finite fields

2008 ◽  
Vol 128 (6) ◽  
pp. 1795-1806 ◽  
Author(s):  
Stéphane Ballet
Keyword(s):  
Finite Fields ◽  
Tensor Rank
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