{
  "abstract": "We prove an equivalence between the existence of a unique Kähler-Einstein metric on a degeneration of Fano varieties and uniform CM minimization. This proves a discretely valued analogue of the (uniform) Yau-Tian-Donaldson conjecture, in the sense of non-Archimedean geometry. As a main tool, we prove that Ding stability of a degeneration implies uniform Ding minimization, proving a converse to work of Blum-Xu. We also prove an analogous result in geometric invariant theory (GIT), stating that uniform GIT height minimization of a family of points is equivalent to GIT stability, proving a converse to work of Wang, Wang-Xu and the author.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39996",
  "author_total": 1,
  "authors": [
    {
      "name": "Gabriel Frey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8r2bbbgn0myaq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39996",
  "fulltext_url": null,
  "id": "8r2bbbgn0myaq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39996",
  "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/2610.39996",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8r2bbbgn0myaq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39996",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39996"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Yau-Tian-Donaldson correspondence for degenerations",
  "title_text": "A Yau-Tian-Donaldson correspondence for degenerations",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/8r2bbbgn0myaq",
  "venue": "arXiv",
  "versions": []
}