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Spectrahedral
representations of plane hyperbolic curves
Mario Kummer, Simone Naldi and Daniel Plaumann |
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Vol. 303 (2019), No. 1, 243–263
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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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Authors |
| Mario Kummer | |
| Institut für Mathematik Technische Universität Berlin Berlin Germany |
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| Simone Naldi | |
| XLIM Université de Limoges Limoges France |
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| Daniel Plaumann | |
| Fakultät für Mathematik Technische Universität Dortmund Dortmund Germany |
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