{
  "abstract": "We study the K-moduli space of Fano threefolds obtained by first blowing up $\\mathbb{P}^3$ along an elliptic quartic curve $C$ and then blowing up a fiber $\\ell_p$ of the exceptional divisor $E \\to C$. We prove that this K-moduli space is isomorphic to a VGIT quotient parametrizing pairs $(C,p)$, with linearization induced by the CM line bundle. In particular, we classify all K-(semi/poly)stable members of this deformation family. The main new ingredients in the proof include the geometry of the Hilbert scheme of elliptic quartic curves, deformation theory of Fano--K3 pairs, and optimal bounds on the local volumes of threefold singularities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30855",
  "author_total": 4,
  "authors": [
    {
      "name": "Ivan Cheltsov"
    },
    {
      "name": "Anne-Sophie Kaloghiros"
    },
    {
      "name": "Robert Śmiech"
    },
    {
      "name": "Junyan Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0jrt5t1gvp0mb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30855",
  "fulltext_url": null,
  "id": "0jrt5t1gvp0mb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30855",
  "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": "W7204908901",
  "pdf_url": "https://arxiv.org/pdf/2608.30855",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0jrt5t1gvp0mb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30855",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30855"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Degenerations of elliptic quartics and K-moduli of Fano threefolds",
  "title_text": "Degenerations of elliptic quartics and K-moduli of Fano threefolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/0jrt5t1gvp0mb",
  "venue": "arXiv",
  "versions": []
}