Spectrahedral representations of plane hyperbolic curves
Algebraic Geometry
2019-12-25 v1 Optimization and Control
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.
Keywords
Cite
@article{arxiv.1807.10901,
title = {Spectrahedral representations of plane hyperbolic curves},
author = {Mario Kummer and Simone Naldi and Daniel Plaumann},
journal= {arXiv preprint arXiv:1807.10901},
year = {2019}
}
Comments
18 pages, 8 figures