In this work we analyze the $ Spin (V) $-structure of the secant variety of lines $\sigma_
{2}(\mathbb {S}) $ to a Spinor variety $\mathbb {S} $ minimally embedded in its spin …

We propose a new approach to the geometry of the four-qubit entanglement classes
depending on parameters. More precisely, we use invariant theory and algebraic geometry …

We investigate the structure of the three-qubit magic Veldkamp line (MVL). This
mathematical notion has recently shown up as a tool for understanding the structures of the …

We introduce the “skew apolarity lemma” and we use it to give algorithms for the skew-
symmetric rank and the decompositions of tensors in∧ d V ℂ with d≤ 3 and dim V ℂ≤ 8 …

Twenty years ago, Cayley's hyperdeterminant, the degree four invariant of the polynomial
ring CŒC2 C2 C2 SL2. C/3, was popularized in modern physics as it separates genuine …

The possible spectra of one-particle reduced density matrices that are compatible with a
pure multipartite quantum system of finite dimension form a convex polytope. We introduce a …

We find expressions of the polynomials defining the dual varieties of Grassmannians Gr (3,
9) and Gr (4, 8) both in terms of the fundamental invariants and in terms of a generic semi …

We present several multipartite quantum systems featuring the same type of genuine
(tripartite) entanglement. Based on a geometric interpretation of the so-called $| W\rangle …

In this review paper I present two geometric constructions of distinguished nature, one is
over the field of complex numbers ℂ C and the other one is over the two elements field 𝔽 2 F …

Borrowing ideas from the relation between simply laced Lie algebras and Dynkin diagrams,
a weighted graph theory representation of quantum information is addressed. In this way …