{
  "abstract": "Let $L$ be a smooth Hermitian holomorphic line bundle on a compact complex manifold $X$ of dimension $n$, and let $r$ be its maximal curvature rank. For every fixed holomorphic vector bundle $E$, we prove $h^q(X,L^p\\otimes E)=O_\\varepsilon(p^{r+\\varepsilon})$ for every $\\varepsilon>0$ and every Dolbeault degree, with the sharp bounds $h^0,h^n=O(p^r)$ at the endpoints. The curvature may have variable rank and arbitrary signature, and no global foliation or Kähler assumption is imposed. The all-degree estimate follows from local rescaling and holomorphic restriction estimates that remain uniform across rank changes. An independent maximum-principle argument locates the maximal rank of a section map at a semipositive curvature point; it yields $κ(L|_{X_0})\\le r$ on each connected component $X_0$ and gives the endpoint bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09295",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiangsen Qin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dh7d44wtnmqgs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09295",
  "fulltext_url": null,
  "id": "dh7d44wtnmqgs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09295",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7220893481",
  "pdf_url": "https://arxiv.org/pdf/2610.09295",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dh7d44wtnmqgs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.09295",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09295"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Dolbeault Cohomology Growth under Curvature Rank Bounds",
  "title_text": "Dolbeault Cohomology Growth under Curvature Rank Bounds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/dh7d44wtnmqgs",
  "venue": "arXiv",
  "versions": []
}