{
  "abstract": "Let $X$ be a smooth complex projective variety of dimension $n$, and let $L$ be an ample Cartier divisor. We prove that $K_X+mL$ is globally generated for every integer $m\\geq\\lceil C_0n\\rceil$, where $C_0=1.77629\\ldots$ is an explicit constant. In particular, $K_X+2nL$ is globally generated. We also prove that if $Z$ is a normal projective variety of dimension $n$ with $K_Z$ Cartier, nef and big, then $|mK_Z|$ defines a birational map for every integer $m\\geq1+\\lceil C_0n+3\\sqrt{2\\mathrm{e}n}\\rceil$. Our main input is a new estimate for the multiplicity of a minimal log canonical center. If $(X,Δ)$ is log canonical near a closed point $x$ but is not klt at $x$, and $W$ is the positive-dimensional minimal log canonical center through $x$, then $2\\overline{e}_1(\\mathfrak m_{W,x})\\leq\\bigl(\\dim W-\\operatorname{lct}_x((X,Δ);\\mathfrak m_x)\\bigr)\\operatorname{mult}_xW$, where $\\overline{e}_1(\\mathfrak m_{W,x})$ is the first normal Hilbert coefficient of the maximal ideal of $\\mathcal O_{W,x}$. This implies $\\operatorname{mult}_xW\\leq \\frac{(a+c)^{a+c}}{a^ac^c}$, where $a:=\\frac{\\dim W-\\operatorname{lct}_x((X,Δ);\\mathfrak m_{x})}{2}$ and $c:=\\operatorname{edim}\\mathcal O_{W,x}-\\dim W$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01574",
  "author_total": 1,
  "authors": [
    {
      "name": "Jingjun Han"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ca5nzkvfxz24f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01574",
  "fulltext_url": null,
  "id": "ca5nzkvfxz24f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01574",
  "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": "W7206172354",
  "pdf_url": "https://arxiv.org/pdf/2609.01574",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ca5nzkvfxz24f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.01574",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01574"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A linear bound for Fujita's freeness conjecture",
  "title_text": "A linear bound for Fujita's freeness conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/ca5nzkvfxz24f",
  "venue": "arXiv",
  "versions": []
}