Generic Spectrahedral Shadows

TL;DR

This paper characterizes the polynomials that vanish on the boundaries of generic spectrahedral shadows, which are projections of linear sections of the positive semidefinite cone, enhancing understanding of their algebraic structure.

Contribution

It provides a new characterization of boundary-vanishing polynomials for generic spectrahedral shadows, advancing the algebraic understanding of these convex sets.

Findings

Identifies polynomials vanishing on spectrahedral shadow boundaries

Provides algebraic conditions for generic spectrahedral shadows

Enhances understanding of convex algebraic geometry

Abstract

Spectrahedral shadows are projections of linear sections of the cone of positive semidefinite matrices. We characterize the polynomials that vanish on the boundaries of these convex sets when both the section and the projection are generic.