PreprintCC BY 4.0arXiv
Nonnegative conorms, regular matroids, and the tropical Schottky problem
Abstract
We prove that a positive-definite quadratic form has nonnegative conorms if and only if it is matroidal, resolving a conjecture of Dutour Sikirić 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.
Related
- Totally nonnegative tropical flags and the totally nonnegative flag Dressian
- Quantitative Rigidity of Ricci Nonnegative Manifolds via the Regular Green Constant
- Spectral Equality for Tropical Totally Nonnegative Matrices: Dominant Cancellation and Newton Polygons
- Freeness of Arrangements with Regular Underlying Matroids
- Logarithmic basis number of graphs and regular matroids
BibTeX
@misc{mandelshtam2026nonnegative,
title = {{Nonnegative conorms, regular matroids, and the tropical Schottky problem}},
author = {Yelena Mandelshtam},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28783},
eprint = {2608.28783},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28783},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonnegative conorms, regular matroids, and the tropical Schottky problem
AU - Yelena Mandelshtam
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28783
UR - https://arxiv.org/abs/2608.28783
AB - We prove that a positive-definite quadratic form has nonnegative conorms if and only if it is matroidal, resolving a conjecture of Dutour Sikirić 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.
ER -