Equations of Tree Tensor Network Varieties
Published in arXiv preprint, 2026
We show that tree tensor network varieties, including tensor train varieties, are general Markov models associated to spaced trees. This allows us to prove that the prime ideals of these varieties are generated by minors of matrix flattenings. In the case of tensor train varieties, we discuss whether these minors form a Gröbner basis and provide a combinatorial method to compute the degree for order 3 tensor trains.
Recommended citation: Serkan Hoşten, Niharika Chakrabarty Paul, Otto T. P. Schmidt and Dmitry Skurt. Equations of Tree Tensor Network Varieties. arXiv:2608.19071 (2026).
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