{
  "abstract": "We introduce the notion of tropical regularity as a generalization of tropical smoothness and present a geometric classification conjecture for tropical regular cycles. Roughly, the conjecture predicts that every regular tuple either forms a regular fibration or descends via a lattice projection to one of finitely many minimal-model cycles. Our main results establish this conjecture in three fundamental cases:unmixed regular tuples $(T,\\ldots,T,[F])$ with $L(T)=\\{0\\}$ and $[F]$ spanning its ambient space; regular tropicalizations of complete intersections with generic coefficients; and regular tropical $2$-cycles satisfying the Hodge index inequality and spanning their ambient space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.24339",
  "author_total": 1,
  "authors": [
    {
      "name": "Linxuan Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ann9cyt90sjf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.24339",
  "fulltext_url": null,
  "id": "8ann9cyt90sjf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.24339",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7165804516",
  "pdf_url": "https://arxiv.org/pdf/2606.24339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ann9cyt90sjf.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:09Z",
      "native_id": "2606.24339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.24339"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Tropical Regularity",
  "title_text": "Tropical Regularity",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/8ann9cyt90sjf",
  "venue": "arXiv",
  "versions": []
}