{
  "abstract": "We give an algebraic proof in characteristic zero of the Miyaoka--Mori criterion: every point of a curve of negative canonical degree on a smooth projective variety lies on a rational curve. Our jet technique gives, in addition, an effective numerical decomposition of the original curve class. For each prescribed point, the decomposition contains a rational curve through that point, with a positive coefficient independent of the point and with anticanonical degree at most $\\dim X+1$. Together with BDPP cone duality, this recovers the projective uniruledness criterion over $\\mathbb C$. The main result of this paper was obtained using the Pharos system. A detailed report on the use of Pharos and on the Lean~4 formalization of the main arguments is given in the Appendix B, written by Bin Dong, Guoxiong Gao, Zeming Sun, and Bin Wu.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28465",
  "author_total": 6,
  "authors": [
    {
      "name": "Bin Dong"
    },
    {
      "name": "Guoxiong Gao"
    },
    {
      "name": "Bin Guo"
    },
    {
      "name": "Zeming Sun"
    },
    {
      "name": "Bin Wu"
    },
    {
      "name": "Song-Yan Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c37vvjk595fj3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28465",
  "fulltext_url": null,
  "id": "c37vvjk595fj3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28465",
  "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"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214210635",
  "pdf_url": "https://arxiv.org/pdf/2609.28465",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c37vvjk595fj3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28465",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28465"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Constructing Rational Curves via Jets on Projective Varieties with Non-Nef Canonical Bundle",
  "title_text": "Constructing Rational Curves via Jets on Projective Varieties with Non-Nef Canonical Bundle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/c37vvjk595fj3",
  "venue": "arXiv",
  "versions": []
}