Tangential weak defectiveness and generic identifiability

TL;DR

This paper studies the uniqueness of tensor decompositions, extending existing theory to non-twd varieties, and proves non-generic identifiability for many partially symmetric tensors.

Contribution

It extends the theory of tensor identifiability to non-twd varieties, demonstrating non-generic identifiability for numerous partially symmetric tensors.

Findings

Proves non-generic identifiability for many partially symmetric tensors

Extends tensor decomposition theory to non-twd varieties

Provides new results on tensor uniqueness in complex spaces

Abstract

We investigate the uniqueness of decomposition of general tensors $T\in {\mathbb C}^{n_1+1}\otimes\cdots\otimes{\mathbb C}^{n_r+1}$ as a sum of tensors of rank $1$. This is done extending the theory developed in a previous paper by the second author to the framework of non twd varieties. In this way we are able to prove the non generic identifiability of infinitely many partially symmetric tensors.