{
  "abstract": "We show that possibly singular threefold flopping contractions are completely classified by their associated derived contraction algebras, considered up to derived Morita equivalence; in contrast to the smooth case the extra derived structure is necessary in general. This extends previous work of the author on simple flops, and follows from a more general theorem about isolated hypersurface singularities. The key new input is to show that derived localisation at a Hochschild class is Morita invariant; this result raises some interesting questions related to the classification of recollements. We also show that derived contraction algebras admit a deformation-theoretic interpretation in families in a general setting that encompasses threefold flops, flips, and divisor-to-curve contractions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24864",
  "author_total": 1,
  "authors": [
    {
      "name": "Matt Booth"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fnr87f67k8den.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24864",
  "fulltext_url": null,
  "id": "fnr87f67k8den",
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  "landing_url": "https://arxiv.org/abs/2610.24864",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
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      "arxiv",
      "math.RT"
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      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  "openalex": "W7223060505",
  "pdf_url": "https://arxiv.org/pdf/2610.24864",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fnr87f67k8den.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24864",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24864"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the classification of threefold flops",
  "title_text": "On the classification of threefold flops",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/fnr87f67k8den",
  "venue": "arXiv",
  "versions": []
}