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# An Algebraic-Geometric Characterization of Tripartite Entanglement

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### Abstract

To characterize entanglement of tripartite $$\mathbb{C}^d\otimes\mathbb{C}^d\otimes\mathbb{C}^d$$ systems, we employ algebraic-geometric tools that are invariants under Stochastic Local Operation and Classical Communication (SLOCC), namely $$k$$-secants and one-multilinear ranks. Indeed, by means of them, we present a classification of tripartite pure states in terms of a finite number of families and subfamilies. At the core of it stands out a fine-structure grouping of three-qutrit entanglement.

### Author and article information

###### Journal
28 June 2021
###### Article
2106.14891