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Abstract
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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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Keywords
real algebraic curves, determinantal representations,
spectrahedra, linear matrix inequalities
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Mathematical Subject Classification 2010
Primary: 14H50, 14P99, 52A10
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Milestones
Received: 28 August 2018
Revised: 30 May 2019
Accepted: 8 June 2019
Published: 21 December 2019
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