Algebraic-geometric characterization of tripartite entanglement

To characterize entanglement of tripartite systems, we employ algebraic-geometric tools that are invariants under stochastic local operation and classical communication, namely -secant varieties 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.