Article Dans Une Revue Pacific Journal of Mathematics Année : 2019

SPECTRAHEDRAL REPRESENTATIONS OF PLANE HYPERBOLIC CURVES

Résumé

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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hal-02436202 , version 1 (12-01-2020)

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Mario Kummer, Simone Naldi, Daniel Plaumann. SPECTRAHEDRAL REPRESENTATIONS OF PLANE HYPERBOLIC CURVES. Pacific Journal of Mathematics, 2019, 303 (1), pp.243-263. ⟨10.2140/pjm.2019.303.243⟩. ⟨hal-02436202⟩
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