{
  "abstract": "Let $ω_{\\mathrm{FS}}$ be the normalized Fubini--Study form on $\\mathbf P^n$, with $n\\geq2$. We prove that the one-pole Lelong-number range in $DMA(\\mathbf P^n,ω_{\\mathrm{FS}})$ is exactly $[0,1]$: for every $λ$ in this interval there is a Green function with a single pole, Monge--Ampère measure equal to the Dirac mass at that pole, and Lelong number $λ$. This answers Question~9 in the survey of Dinew--Guedj--Zeriahi, where the problem is attributed to Coman and Guedj. The construction adapts Li and Xia's local zero-Lelong-number scheme through variable degrees and homogeneous finite stages, while also establishing the exact Lelong number and membership in the global $DMA$ class. We then study the relation between the one-pole range $\\mathcal R_α(x)$ and the Seshadri interval $[0,\\varepsilon(α,x)]$. An application of Koike's equivalence theorem gives a point on a degree-one del Pezzo surface where the Seshadri endpoint is not attained. Conversely, a finite-pullback criterion and an explicit finite morphism show that every ample rational class on a product of projective spaces realizes its full Seshadri interval at every point.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02513",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiangsen Qin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4hp9rgnqcfvkj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02513",
  "fulltext_url": null,
  "id": "4hp9rgnqcfvkj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02513",
  "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": "W7207638143",
  "pdf_url": "https://arxiv.org/pdf/2609.02513",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4hp9rgnqcfvkj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02513",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02513"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Prescribed Lelong Numbers for One-Pole Green Functions on Complex Projective Space",
  "title_text": "Prescribed Lelong Numbers for One-Pole Green Functions on Complex Projective Space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/4hp9rgnqcfvkj",
  "venue": "arXiv",
  "versions": []
}