{
  "abstract": "Let $X$ be a smooth projective toric variety of dimension $n\\geq1$ over an algebraically closed field of characteristic zero, let $\\mathcal E$ be a toric vector bundle of rank $r\\geq2$, and let $π\\colon Y=\\mathbb P_X(\\mathcal E)\\to X$ be the projective bundle of one-dimensional quotients. Write an ample line bundle on $Y$ as $A=\\mathcal O_Y(a)\\otimesπ^*L$, with $a\\geq1$. We record a blow-up argument proving that $K_Y+mA$ is globally generated whenever an integer $m$ satisfies $ma\\geq r$ and $mδ(A)>n$, where $δ(A)$ is a positive integer obtained from the degrees of $A$ on the invariant quotient sections over the torus-invariant curves of $X$. In particular, $K_Y+mA$ is globally generated for $m\\geq n+1$ and $ma\\geq r$. Consequently every projectivized toric vector bundle satisfies Fujita's freeness conjecture. The uniform bound is sharp. We also formulate the result as a global-generation theorem for adjoint symmetric powers of $\\mathcal E$ and explain its relation with the Seshadri-constant results of Hering--Mustaţă--Payne and Fulger--Murayama. ChatGPT (OpenAI) was used to assist with mathematical discussion, language, and bibliographic searches.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28438",
  "author_total": 1,
  "authors": [
    {
      "name": "Antonio Laface"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cwma81svgtjys.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28438",
  "fulltext_url": null,
  "id": "cwma81svgtjys",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28438",
  "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": "W7204770752",
  "pdf_url": "https://arxiv.org/pdf/2608.28438",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cwma81svgtjys.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.28438",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28438"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Fujita freeness for projectivized toric vector bundles",
  "title_text": "Fujita freeness for projectivized toric vector bundles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/cwma81svgtjys",
  "venue": "arXiv",
  "versions": []
}