paper

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

arXiv:2412.02319 · doi:10.1016/j.laa.2025.09.006

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 Å ivic.

34 pages, 1 figure

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