The Algebraic Boundary of SO(2)-Orbitopes

Abstract

Let $X\subset\A^{2r}$ be a real curve embedded into an even-dimensional affine space. In the main result of this paper, we characterise when the r-th secant variety to $X$ is an irreducible component of the algebraic boundary of the convex hull of the real points $X(\mathbb{R})$ of $X$. This fact is then applied to 4-dimensional SO(2)-orbitopes and to the so called Barvinok-Novik orbitopes to study when they are basic closed as semi-algebraic sets. In the case of 4-dimensional SO(2)-orbitopes, we find all irreducible components of their algebraic boundary.

17 pages, 1 figure

References in corpus (1)

• Positive Polynomials and Projections of Spectrahedra

Cited by in corpus (1)

• Abstract Operator Systems over the Cone of Positive Semidefinite Matrices