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arXiv · 2412.02319

(Positive) Quadratic Determinantal Representations of Quartic Curves and the Robinson Polynomial

Clemens Brüser·Mario Kummer
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Abstract

We prove that every real nonnegative ternary quartic whose complex zero set is smooth can be represented as the determinant of a symmetric matrix with quadratic entries which is everywhere positive semidefinite. We show that the corresponding statement fails for the Robinson polynomial, answering a question by Buckley and \v{S}ivic.

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Clemens Brüser, Mario Kummer. 2024-12-03. (Positive) Quadratic Determinantal Representations of Quartic Curves and the Robinson Polynomial. https://doi.org/10.1016/j.laa.2025.09.006

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