1. On Comon's and Strassen's conjectures
- Author
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Casarotti, Alex, Massarenti, Alex, and Mella, Massimiliano
- Subjects
Mathematics - Algebraic Geometry ,Primary 15A69, 15A72, 11P05, Secondary 14N05, 15A69 - Abstract
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., Comment: 12 pages
- Published
- 2018