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Nonnegative conorms, regular matroids, and the tropical Schottky problem — arXiv:2608.28783

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.28783
License (as archived): CC0-1.0
Archived: 2026-10-17T09:31:18.534Z
SHA-256 of the archived text: c3e06077f3eeadd95a480d95273df3253cc1b558776ed80c86309ee66fdc6d90
Stable URL of this page: https://metraipolis.com/documento/dc_9743a50fb235

How to cite

Nonnegative conorms, regular matroids, and the tropical Schottky problem — arXiv:2608.28783 — arXiv (en), https://arxiv.org/abs/2608.28783 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_9743a50fb235 (Metraipolis archive dc_9743a50fb235, sha256 c3e06077f3eeadd95a480d95273df3253cc1b558776ed80c86309ee66fdc6d90)

BibTeX

@misc{dc9743a50fb235,
  title = {Nonnegative conorms, regular matroids, and the tropical Schottky problem — arXiv:2608.28783},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.28783},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_9743a50fb235; sha256 c3e06077f3eeadd95a480d95273df3253cc1b558776ed80c86309ee66fdc6d90},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.28783. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-01 in math.CO).
Categorie arXiv: Algebraic Geometry (math.AG) ; Combinatorics (math.CO); Metric Geometry (math.MG).
Pagina del lavoro: https://arxiv.org/abs/2608.28783 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T09:02:28.877Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).