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math.AG2025
Adjoints of Polytopes: Determinantal Representations and Smoothness
Clemens Brüser, Mario Kummer, Dmitrii Pavlov
In this article we study determinantal representations of adjoint hypersurfaces of polytopes. We prove that adjoint polynomials of all polygons can be represented as determinants o…
math.AG2024
(Positive) Quadratic Determinantal Representations of Quartic Curves and the Robinson Polynomial
Clemens Brüser, Mario Kummer
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 ev…