{
  "abstract": "Di Nezza--Guedj--Lu asked whether local Arnold multiplicities under maximal weak twisted Kähler--Ricci flow with fixed cohomology class satisfy $λ(φ_t,x)=\\max\\{λ(φ_0,x)-t,0\\}$. We construct counterexamples with analytic initial singularities in every dimension $n\\ge2$. On the Hirzebruch surface $\\mathbb F_e$, $e\\ge2$, the initial current $[S]+(e+1)[F]$ yields $λ(φ_t,x)=1/2-t/e$ for $x\\in S\\setminus F$ and $0<t<e/2$, where $S$ is the negative section and $F$ a fibre. Products with smooth stationary factors give higher-dimensional examples. The Zariski negative part of $\\{S\\}+\\{F\\}$, the reduced support class, forces extra divisor mass. For pure divisorial data with simple normal crossings support, a smooth semipositive representative of the reduced support class's positive part gives exact short-time formulas. On one surface we construct flows with identical initial current germs, background data and global initial Arnold multiplicity, but different local rates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30302",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiangsen Qin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/292nb7vhfhn1q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30302",
  "fulltext_url": null,
  "id": "292nb7vhfhn1q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30302",
  "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.AP"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7204875218",
  "pdf_url": "https://arxiv.org/pdf/2608.30302",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/292nb7vhfhn1q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2608.30302",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30302"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Failure of the local decay formula for Arnold multiplicities under twisted Kähler--Ricci flow",
  "title_text": "Failure of the local decay formula for Arnold multiplicities under twisted Kähler--Ricci flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/292nb7vhfhn1q",
  "venue": "arXiv",
  "versions": []
}