Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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M. Kummer - S. Naldi - D. Plaumann

Spectrahedral representations of plane hyperbolic curves

created by naldi on 23 Sep 2018
modified on 18 May 2020


Published Paper

Inserted: 23 sep 2018
Last Updated: 18 may 2020

Journal: Pac. J. Math.
Volume: 1
Pages: 243–263
Year: 2019
Doi: 10.2140/pjm.2019.303.243

ArXiv: 1807.10901 PDF
Links: Publisher page


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.

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