{
  "abstract": "We determine the strictly semistable boundary of the GIT compactification of quintic threefolds for the natural $\\mathrm{SL}(5)$-action on $\\mathbb{P}(\\mathrm{Sym}^5\\mathbb{C}^5)$. Using the Hilbert--Mumford criterion and exact integer linear algebra, we enumerate thirty-eight maximal strictly semistable monomial supports up to coordinate permutation. After taking S-equivalence into account, their images in the GIT quotient reduce to twenty-one families, and we prove that these are precisely the irreducible components of the GIT boundary, with dimensions ranging from $1$ to $24$. Version 1 incorrectly identified the thirty-eight maximal supports with thirty-eight irreducible boundary components by overlooking S-equivalence; that claim is withdrawn and replaced by the twenty-one-component classification proved here. Four components recover Lakhani's first-level families and seventeen are additional components. For each component we construct a general polystable normal form and determine its generic connected projective stabilizer. Pairwise nonconjugacy of the resulting one-dimensional tori, together with Luna's etale slice theorem, excludes containments between distinct components. We also describe the singularities of general closed-orbit representatives. Their isolated singularities fall into exactly eleven weighted-homogeneous local families whose normalized weights occur in Yonemura's list, and every component has global minimal exponent $1$, the critical value $(n+1)/d$ for quintic hypersurfaces in $\\mathbb{P}^4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.00309",
  "author_total": 1,
  "authors": [
    {
      "name": "Yasutaka Shibata"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6k110ctgdnaqr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.00309",
  "fulltext_url": null,
  "id": "6k110ctgdnaqr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.00309",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7160146556",
  "pdf_url": "https://arxiv.org/pdf/2605.00309",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6k110ctgdnaqr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2605.00309",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.00309"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The GIT Boundary of Quintic Threefolds",
  "title_text": "The GIT Boundary of Quintic Threefolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/6k110ctgdnaqr",
  "venue": "arXiv",
  "versions": []
}