{
  "abstract": "We disprove Wahl's 1993 vanishing conjecture, open for more than thirty years, which asserts that $c_2^w(X)=0$ for every nonquotient normal surface singularity. Let $C$ be a smooth projective curve with a nontrivial involution having $r>0$ fixed points, and put $d=2g(C)-2$. If $d>r$, the union of the diagonal and the graph of the involution in $C\\times C$ has negative definite intersection matrix and can be analytically contracted to a normal surface singularity $(X,o)$. A direct relative Chern-class computation and Wahl's residue formula give $c_2^w(X)=-r(d+r)/(d-r)$. An explicit curve of genus four gives $c_2^w(X)=-4$. Branched double covers of a fixed curve of genus two yield examples with $c_2^w(X_m)=-2m(m+1)$, so these values are unbounded below. We give the construction and intersection calculations in detail, as well as a line-bundle filtration realizing the negative value.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25606",
  "author_total": 1,
  "authors": [
    {
      "name": "Rong Du"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e3ck0sp3v01pr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25606",
  "fulltext_url": null,
  "id": "e3ck0sp3v01pr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25606",
  "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": "W7223065150",
  "pdf_url": "https://arxiv.org/pdf/2610.25606",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e3ck0sp3v01pr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25606",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25606"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Negative Values of Wahl's Second Chern Number for Normal Surface Singularities",
  "title_text": "Negative Values of Wahl's Second Chern Number for Normal Surface Singularities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/e3ck0sp3v01pr",
  "venue": "arXiv",
  "versions": []
}