Spectrahedral representations of plane hyperbolic curves
arXiv:1807.10901 · doi:10.2140/pjm.2019.303.243
Abstract
We describe a new method for constructing a spectrahedral representation of the hyperbolicity region of a hyperbolic curve in the real projective plane. As a consequence, we show that if the curve is smooth and defined over the rational numbers, then there is a spectrahedral representation with rational matrices. This generalizes a classical construction for determinantal representations of plane curves due to Dixon and relies on the special properties of real hyperbolic curves that interlace the given curve.
18 pages, 8 figures