{
  "abstract": "Let $S=\\mathbb K[x_1,\\cdots,x_n]$ be a polynomial ring in $n$ variables with positive integer weights over a field $\\mathbb K$ of characteristic zero. Let $f\\in S$ be a weighted homogeneous polynomial such that the Jacobian algebra $$A=\\left.S \\middle/ \\left(\\frac{\\partial f}{\\partial x_1},\\cdots,\\frac{\\partial f}{\\partial x_n}\\right)\\right.$$ is a finite-dimensional $\\mathbb K$-vector space. We prove that $A$ has no nonzero negative weight derivation, which confirms a conjecture of the third author. An immediate consequence of this conjecture is the micro-local characterization of quasi-homogeneous singularities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25615",
  "author_total": 4,
  "authors": [
    {
      "name": "Bingyi Chen"
    },
    {
      "name": "Zhiwen Liu"
    },
    {
      "name": "Stephen S. -T. Yau"
    },
    {
      "name": "Huaiqing Zuo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3y4s1e9effys2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25615",
  "fulltext_url": null,
  "id": "3y4s1e9effys2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25615",
  "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.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7223063472",
  "pdf_url": "https://arxiv.org/pdf/2610.25615",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3y4s1e9effys2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25615",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25615"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Non-existence of negative weight derivations on Jacobian algebras",
  "title_text": "Non-existence of negative weight derivations on Jacobian algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/3y4s1e9effys2",
  "venue": "arXiv",
  "versions": []
}