scholarly journals On the ideals and singularities of secant varieties of Segre varieties

2007 ◽  
Vol 39 (4) ◽  
pp. 685-697 ◽  
Author(s):  
J. M. Landsberg ◽  
Jerzy Weyman
2008 ◽  
Vol 361 (02) ◽  
pp. 767-792 ◽  
Author(s):  
Hirotachi Abo ◽  
Giorgio Ottaviani ◽  
Chris Peterson

2002 ◽  
Vol 355 (1-3) ◽  
pp. 263-285 ◽  
Author(s):  
M.V. Catalisano ◽  
A.V. Geramita ◽  
A. Gimigliano

2005 ◽  
Vol 201 (1-3) ◽  
pp. 367-380 ◽  
Author(s):  
M.V. Catalisano ◽  
A.V. Geramita ◽  
A. Gimigliano

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 217 ◽  
Author(s):  
Alex Casarotti ◽  
Alex Massarenti ◽  
Massimiliano Mella

Comon’s conjecture on the equality of the rank and the symmetric rank of a symmetric tensor, and Strassen’s conjecture on the additivity of the rank of tensors are two of the most challenging and guiding problems in the area of tensor decomposition. We survey the main known results on these conjectures, and, under suitable bounds on the rank, we prove them, building on classical techniques used in the case of symmetric tensors, for mixed tensors. Finally, we improve the bound for Comon’s conjecture given by flattenings by producing new equations for secant varieties of Veronese and Segre varieties.


2004 ◽  
Vol 4 (4) ◽  
pp. 397-422 ◽  
Author(s):  
J. M. Landsberg ◽  
L. Manivel

2011 ◽  
Vol 215 (5) ◽  
pp. 1040-1052 ◽  
Author(s):  
Tahereh Aladpoosh ◽  
Hassan Haghighi

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