{
  "abstract": "We show that any big line bundle on a smooth projective variety admits a special Fujita approximation: the volume and the first Riemann-Roch coefficient are both approximated by those of ample $\\mathbb{Q}$-line bundles on higher models. Exploiting previous works by Boucksom, Jonsson and Li, we solve the Boucksom-Jonsson Regularization Conjecture on the Non-Archimedean entropy functional. As a main consequence, we obtain a solution to the (uniform version of the) Yau-Tian-Donaldson Conjecture: a polarized smooth projective variety $(X,L)$ admits a cscK metric if and only if it is $\\mathrm{Aut}^\\circ(X,L)$-uniformly $K$-stable. This extends the known Yau-Tian-Donaldson correspondence for smooth Fano varieties.",
  "abstract_shown": true,
  "affiliations": [
    "Università di Roma Tor Vergata , Via della Ricerca Scientifica 1 , 00133 , Roma , Italy"
  ],
  "article_type": null,
  "arxiv": "2605.30063",
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Antonio Trusiani",
      "orcid": "0000-0002-1936-2162"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5pe2ej3jx5hsa.bib",
  "cited_by": 13,
  "doi": "10.48550/arxiv.2605.30063",
  "fulltext_url": null,
  "id": "5pe2ej3jx5hsa",
  "issns": [
    "2331-8422"
  ],
  "landing_url": "https://arxiv.org/abs/2605.30063",
  "language": "en",
  "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"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7162781108",
  "pdf_url": "https://arxiv.org/pdf/2605.30063",
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-28",
  "publisher": "Cornell University",
  "ris": "https://research.draconitic.com/paper/5pe2ej3jx5hsa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2605.30063",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.30063"
    },
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W7162781108",
      "source": "openalex",
      "url": "https://arxiv.org/abs/2605.30063"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A solution to the Yau-Tian-Donaldson Conjecture through Special Fujita Approximations",
  "title_text": "A solution to the Yau-Tian-Donaldson Conjecture through Special Fujita Approximations",
  "type": "preprint",
  "updated_at": "2026-11-08T13:20:36Z",
  "url": "https://research.draconitic.com/paper/5pe2ej3jx5hsa",
  "venue": "arXiv",
  "versions": []
}