Tensor ranks on tangent developable of Segre varieties

Abstract

We describe the stratification by tensor rank of the points belonging to the tangent developable of any Segre variety. We give algorithms to compute the rank and a decomposition of a tensor belonging to the secant variety of lines of any Segre variety. We prove Comon's conjecture on the rank of symmetric tensors for those tensors belonging to tangential varieties to Veronese varieties.

arXiv commentRemarks 1 and 2 modified with respect to the published version. No modifications in the main Theorem and its proof

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• On best rank-2 and rank-(2,2,2) approximations of order-3 tensors
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• Border Ranks of Positive and Invariant Tensor Decompositions: Applications to Correlations
• On Comon's and Strassen's conjectures
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