{
  "abstract": "This is the first in a series of papers on counting surfaces on Calabi-Yau 4-folds.To complement the Hilbert scheme of 2-dimensional subschemes, we introduce two types of moduli spaces of stable pairs.We show that all three moduli spaces are related by GIT wall-crossing and parametrize stable objects in the bounded derived category.We construct reduced Oh-Thomas virtual cycles on the moduli spaces via Kiem-Li cosection localization and prove that they are deformation invariant along Hodge loci.As an application, we show that the variational Hodge conjecture holds for any family of Calabi-Yau 4-folds supporting a nonzero reduced virtual cycle.1. Introduction 2431 2. Stable pairs 2443 3. Moduli spaces 2453 4. Virtual cycles 2481 5. Deformation invariance 2513 Appendix A. Reductions via .1/-shifted 1-forms 2529 Appendix B. Moduli stacks of semistable sheaves 2543 Appendix C. Orientations for relative moduli spaces 2554",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, University of Michigan, Ann Arbor, MI, United States",
    "Mathematical Institute, Utrecht University, Utrecht, Netherlands",
    "June E Huh Center for Mathematical Challenges, Korea Institute for Advanced Study, Seoul, South Korea"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
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      "name": "Younghan Bae",
      "orcid": "0000-0002-3984-1742"
    },
    {
      "affs": [
        1
      ],
      "name": "Martijn Kool",
      "orcid": "0000-0002-9985-6698"
    },
    {
      "affs": [
        2
      ],
      "name": "Hyeonjun Park",
      "orcid": "0000-0001-8258-2355"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/51aqh3a9trt7h.bib",
  "cited_by": 20,
  "doi": "10.2140/gt.2026.30.2431",
  "fulltext_url": null,
  "id": "51aqh3a9trt7h",
  "issns": [
    "1364-0380",
    "1465-3060"
  ],
  "landing_url": "https://doi.org/10.2140/gt.2026.30.2431",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
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      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  "pdf_url": "https://msp.org/gt/2026/30-7/gt-v30-n7-p01-s.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-13",
  "publisher": "Mathematical Sciences Publishers",
  "ris": "https://research.draconitic.com/paper/51aqh3a9trt7h.ris",
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      "url": "https://doi.org/10.2140/gt.2026.30.2431"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic Geometry and Number Theory",
      "subfield": "geometry-topology"
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  ],
  "title": "Counting surfaces on Calabi–Yau 4-folds, I : Foundations",
  "title_text": "Counting surfaces on Calabi–Yau 4-folds, I : Foundations",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:20:59Z",
  "url": "https://research.draconitic.com/paper/51aqh3a9trt7h",
  "venue": "Geometry & Topology",
  "versions": []
}