{
  "abstract": "A line bundle is $\\otimes$-generating if its powers generate the derived category of perfect complexes. Refining the derived Nakai--Moishezon criterion of Ito--Olander, we characterize $\\otimes$-generating line bundles on proper toric varieties by a combinatorial criterion on the fan, leading to the notion of $\\otimes$-generating fans characterizing $\\otimes$-generating canonical bundles. Furthermore, we prove an analogue of Kleiman's criterion of ampleness for $\\otimes$-generation. As applications, we provide several examples including: (i) smooth proper fourfolds with no $\\otimes$-generating line bundle, by showing that products of two or more positive-dimensional proper toric varieties admit a $\\otimes$-generating line bundle only when they are projective, (ii) families of smooth non-projective proper threefolds with $\\otimes$-generating canonical bundles. Finally, we study subvarieties obstructing $\\otimes$-generation of canonical bundles and implications to autoequivalences of derived categories.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22279",
  "author_total": 3,
  "authors": [
    {
      "name": "Daigo Ito"
    },
    {
      "name": "Michael R. Zeng"
    },
    {
      "name": "Xiangru Zeng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9tdav0fzzmxyg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22279",
  "fulltext_url": null,
  "id": "9tdav0fzzmxyg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22279",
  "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.CO"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7222696012",
  "pdf_url": "https://arxiv.org/pdf/2610.22279",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9tdav0fzzmxyg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22279",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22279"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Tensor-generating line bundles on toric varieties",
  "title_text": "Tensor-generating line bundles on toric varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/9tdav0fzzmxyg",
  "venue": "arXiv",
  "versions": []
}