{
  "abstract": "Mustafin varieties provide a framework for degenerating the projective plane together with marked points, governed by the combinatorics of Bruhat-Tits buildings. Such limit objects are parametrized by the boundary points of a projective compactification of the moduli space of $n$ points in $\\mathbb{P}^2$ constructed by Schaffler-Tevelev. In this paper, we study the locus of this compactification generically parametrizing self-dual configurations, or equivalently, six points lying on a conic. We prove that this locus is a tropical compactification of the moduli space of self-dual configurations, with associated fan a refinement of the self-dual tropical Grassmannian introduced by Geiger-Hashimoto-Sturmfels-Vlad. We show that this compactification is a blow up of $\\overline{\\mathrm{M}}_{0,6}$ and we classify the objects it parametrizes: degenerations of $\\mathbb{P}^2$ equipped with a stable $6$-pointed rational curve that records the limiting conic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35060",
  "author_total": 2,
  "authors": [
    {
      "name": "Alheydis Geiger"
    },
    {
      "name": "Luca Schaffler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0057tz3r9b3hc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35060",
  "fulltext_url": null,
  "id": "0057tz3r9b3hc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35060",
  "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.AG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.35060",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0057tz3r9b3hc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35060",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35060"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Mustafin degenerations of six points in the projective plane and self-duality",
  "title_text": "Mustafin degenerations of six points in the projective plane and self-duality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/0057tz3r9b3hc",
  "venue": "arXiv",
  "versions": []
}