{
  "abstract": "We fully classify vector bundles of critical rank on normal affine surfaces and threefolds over algebraically closed fields via their Chern classes. We also prove existence of rank $2$ bundles on threefolds with prescribed first and second motivic Chern classes. The main input is the motivic filtration on algebraic $K$-theory: its third piece is generated by smooth closed points and is identified with motivic cohomology by the third Chern class.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22679",
  "author_total": 2,
  "authors": [
    {
      "name": "Jean Fasel"
    },
    {
      "name": "Maria Yakerson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/87y2fa0t0ch64.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22679",
  "fulltext_url": null,
  "id": "87y2fa0t0ch64",
  "issns": [],
  "landing_url": "https://hal.science/hal-05820411v1",
  "language": "en",
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
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      "arxiv",
      "math.AT"
    ],
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      "arxiv",
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      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  "openalex": "W7222914924",
  "pdf_url": "https://arxiv.org/pdf/2610.22679",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/87y2fa0t0ch64.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:59Z",
      "native_id": "hal-05820411",
      "source": "hal",
      "url": "https://hal.science/hal-05820411v1"
    },
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.22679",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22679"
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  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Vector bundles on singular surfaces and threefolds",
  "title_text": "Vector bundles on singular surfaces and threefolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/87y2fa0t0ch64",
  "venue": "HAL",
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}