{
  "abstract": "In this article we prove that the adjoint polynomial of arbitrary convex polytopes is up to scaling uniquely determined by vanishing to the right order on the polytopes residual arrangement. This answers a problem posed by Kohn and Ranestad [9, Problem 2] and generalizes their main Theorem [9, Theorem 1] to non-simple polytopes. We furthermore prove that the adjoint polynomial is already characterized by vanishing to the right order on a zero-dimensional subset of the residual arrangement.",
  "abstract_shown": true,
  "affiliations": [
    "Technische Universität Dresden, Germany",
    "Max Planck Institute for Mathematics in the Sciences, Leipzig, and Georg-August-Universität Göttingen, Germany"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Clemens Brüser"
    },
    {
      "affs": [
        1
      ],
      "name": "Julian Weigert"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ebndmwskycnw.bib",
  "cited_by": 0,
  "doi": "10.5802/alco.516",
  "fulltext_url": null,
  "id": "4ebndmwskycnw",
  "issns": [
    "2589-5486"
  ],
  "landing_url": "https://alco.centre-mersenne.org/articles/10.5802/alco.516/",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W4416363730",
  "pdf_url": "https://alco.centre-mersenne.org/item/10.5802/alco.516.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": "MathDoc/Centre Mersenne",
  "ris": "https://research.draconitic.com/paper/4ebndmwskycnw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:25Z",
      "native_id": "10.5802/alco.516",
      "source": "crossref",
      "url": "https://alco.centre-mersenne.org/articles/10.5802/alco.516/"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic Geometry and Number Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Geometry of Adjoint Hypersurfaces for Polytopes",
  "title_text": "Geometry of Adjoint Hypersurfaces for Polytopes",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:25Z",
  "url": "https://research.draconitic.com/paper/4ebndmwskycnw",
  "venue": "Algebraic Combinatorics",
  "versions": []
}