Complex Algebraic Geometry Applied to Integrable Dynamics: Concrete Examples and Open Problems

2018 ◽  
pp. 277-288
Author(s):  
E. Previato
Keyword(s):  
Algebraic Geometry ◽  
Open Problems ◽  
Integrable Dynamics

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 Open problems in Algebraic Geometry

2001 ◽  
Vol 125 (1) ◽  
pp. 1-22 ◽  
Author(s):  
S.J. Edixhoven ◽  
B.J.J. Moonen ◽  
F. Oort
Keyword(s):  
Algebraic Geometry ◽  
Open Problems
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