{
  "abstract": "Let $k$ be an algebraically closed field of characteristic $0$ or $p\\neq3$. We construct a terminal projective 4-fold $X$ and an ample Cartier divisor $D$ such that \\[ 3K_X\\sim0,\\qquad D-K_X\\ \\text{is ample},\\qquad H^0(X,D)=0. \\] In char 0, this disproves Ambro--Kawamata effective non-vanishing conjecture. From this example we construct a smooth projective 4-fold $Y$ with a semiample and big Cartier divisor $D_Y$ such that $D_Y-K_Y$ is basepoint-free and big, and $H^0(Y,D_Y)=0$. We also construct a Gorenstein terminal 6-fold with $K\\sim0$, other geometric avatars, and a terminal order-5 Jacobian quotient.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09270",
  "author_total": 1,
  "authors": [
    {
      "name": "Rahul Ajit"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7rpt811321q25.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09270",
  "fulltext_url": null,
  "id": "7rpt811321q25",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09270",
  "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": "W7220971080",
  "pdf_url": "https://arxiv.org/pdf/2610.09270",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7rpt811321q25.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.09270",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09270"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Counterexamples to the Ambro--Kawamata effective non-vanishing conjecture",
  "title_text": "Counterexamples to the Ambro--Kawamata effective non-vanishing conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/7rpt811321q25",
  "venue": "arXiv",
  "versions": []
}