Classification and degenerations of small minimal border rank tensors via modules

2024/09/09 by Jakub Jagiełła, Jagiełła, Jakub, Joachim Jelisiejew +1 · 1 citation
Mathematics · #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2409.06025

Abstract

We give a self-contained classification of 1_*-generic minimal border rank tensors in ℂ^m ⊗ ℂ^m ⊗ ℂ^m for m ≤ 5. Together with previous results, this gives a classification of all minimal border rank tensors in ℂ^m ⊗ ℂ^m ⊗ ℂ^m for m ≤ 5: there are 107 isomorphism classes (only 37 up to permuting factors). We fully describe possible degenerations among the tensors. We prove that there are no 1-degenerate minimal border rank tensors in ℂ^m ⊗ ℂ^m ⊗ ℂ^m for m ≤ 4.

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