{
  "abstract": "We show that the polar degrees of the coordinate-wise inverse of a linear subspace $L \\subseteq \\mathbb{P}^n$ are given by the coefficients of a substitution of the reduced characteristic polynomial of the associated matroid $\\mathrm{M}(L)$. Our proof connects the geometry of conormal varieties of reciprocal linear spaces to the combinatorial conormal fan of $\\mathrm{M}(L)$. As a corollary, we settle two open conjectures regarding matroid discriminants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.26281",
  "author_total": 3,
  "authors": [
    {
      "name": "Clara Briand"
    },
    {
      "name": "Leonie Kayser"
    },
    {
      "name": "Julian Weigert"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5mqng3z2r3kwt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.26281",
  "fulltext_url": null,
  "id": "5mqng3z2r3kwt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.26281",
  "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.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7166036270",
  "pdf_url": "https://arxiv.org/pdf/2606.26281",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5mqng3z2r3kwt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2606.26281",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.26281"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Polar Degrees of Matroids",
  "title_text": "Polar Degrees of Matroids",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/5mqng3z2r3kwt",
  "venue": "arXiv",
  "versions": []
}