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arXiv · 2608.28783

Nonnegative conorms, regular matroids, and the tropical Schottky problem

Yelena Mandelshtam
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Abstract

We prove that a positive-definite quadratic form has nonnegative conorms if and only if it is matroidal, resolving a conjecture of Dutour Sikiri\'c and Kummer. We show that the positive conorm support determines a regular matroid, and the positive conorms are the coefficients of a unimodular integral decomposition of the form. As a result, we show that a positive-definite form lies in the tropical Schottky locus if and only if its conorms are nonnegative and its positive conorm support matroid is cographic. This answers a question of Chua, Kummer, and Sturmfels and provides algorithms for the tropical Schottky decision and recovery problems in every genus.

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Yelena Mandelshtam. 2026-08-28. Nonnegative conorms, regular matroids, and the tropical Schottky problem. https://arxiv.org/abs/2608.28783

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