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
Keyword(s):  
Secant Varieties ◽  
Segre Varieties

scholarly journals Induction for secant varieties of Segre varieties

2008 ◽  
Vol 361 (02) ◽  
pp. 767-792 ◽  
Author(s):  
Hirotachi Abo ◽  
Giorgio Ottaviani ◽  
Chris Peterson
Keyword(s):  
Secant Varieties ◽  
Segre Varieties

scholarly journals Ranks of tensors, secant varieties of Segre varieties and fat points

2002 ◽  
Vol 355 (1-3) ◽  
pp. 263-285 ◽  
Author(s):  
M.V. Catalisano ◽  
A.V. Geramita ◽  
A. Gimigliano
Keyword(s):  
Secant Varieties ◽  
Fat Points ◽  
Segre Varieties

scholarly journals Higher secant varieties of the Segre varieties P1×⋯×P1

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

scholarly journals On Comon’s and Strassen’s Conjectures

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 217 ◽  
Author(s):  
Alex Casarotti ◽  
Alex Massarenti ◽  
Massimiliano Mella
Keyword(s):  
Tensor Decomposition ◽  
Symmetric Tensor ◽  
Symmetric Tensors ◽  
Secant Varieties ◽  
Segre Varieties

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.

scholarly journals On the Ideals of Secant Varieties of Segre Varieties

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

scholarly journals On the dimension of higher secant varieties of Segre varieties Pn×⋯×Pn

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