{
  "abstract": "We study logarithmic vector fields on exceptional cycles through finite-dimensional representations and recover Laufer's classification of taut normal complex surface singularities. For graphs with two nodes, restriction maps define representations of a fixed quiver, with dimensions bounded independently of the number of components and their self-intersections. We identify restriction cohomology with an extension group and use interval decomposition to reduce its vanishing to interpolation on a rational chain. These calculations determine the classification conditions, and vanishing on every analytic realization proves sufficiency, including the nonrational cases. The obstruction cycles also give a uniform criterion: a graph is taut if and only if $H^1(5E,S_X|_{5E})=0$ for every analytic realization, where $S_X$ is the ambient logarithmic tangent bundle. We prove that five is the smallest positive integer for which this criterion holds for all graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25654",
  "author_total": 2,
  "authors": [
    {
      "name": "Heesang Park"
    },
    {
      "name": "Dongsoo Shin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fk398fgcnjgm0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25654",
  "fulltext_url": null,
  "id": "fk398fgcnjgm0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25654",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223048486",
  "pdf_url": "https://arxiv.org/pdf/2610.25654",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fk398fgcnjgm0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25654",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25654"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The classification of taut surface singularities via representations from logarithmic vector fields",
  "title_text": "The classification of taut surface singularities via representations from logarithmic vector fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/fk398fgcnjgm0",
  "venue": "arXiv",
  "versions": []
}