{
  "abstract": "For a holonomic $D$-module, we consider the extended tropicalization of the reduced $L$-characteristic fiber along the family $L_s=F+(s-1)V_Y$. For $A$-hypergeometric systems, this tropical fiber determines the complete $(A,L)$-umbrella and hence recovers the classical slopes. We extend this result to holonomic binomial $D$-modules, for which the tropical jump parameters are exactly the classical slopes at the origin. As an application, a holonomic binomial $D$-module is regular holonomic if and only if there are no tropical jumps along any coordinate subspace.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41587",
  "author_total": 1,
  "authors": [
    {
      "name": "Jen-Chieh Hsiao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0qw39znapdsax.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41587",
  "fulltext_url": null,
  "id": "0qw39znapdsax",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41587",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41587",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0qw39znapdsax.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41587",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41587"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Extended Tropical Characteristic Fibers and Slopes of Binomial D-Modules",
  "title_text": "Extended Tropical Characteristic Fibers and Slopes of Binomial D-Modules",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/0qw39znapdsax",
  "venue": "arXiv",
  "versions": []
}