{
  "abstract": "Let $B$ be a complex manifold and $f:\\bX\\to B$ a derived \\textit{complex-analytic} (not necessarily \\textit{algebraic}) space with an oriented relative $(-2)$-shifted symplectic structure. We suppose that the closed symplectic form is locally exact in the completed relative de Rham complex, and construct a derived smooth manifold over $B$, independent of additional choices. When $f$ is proper and oriented, this gives integral virtual fundamental classes on its fibres. Our argument is heavily based on the strategy of Borisov-Joyce who already solved the \\textit{algebraic} version of this problem, and uses \\textit{derived differential geometry}. The proof also contains a relative analytic Darboux theorem a-la Brav-Bussi-Joyce, and has a natural analogue in Borel-Moore homology. We provide applications to complex-analytic enumerative geometry: in particular, to counting Pandharipande-Thomas pairs on compact and non-compact complex-analytic Calabi-Yau $4$-folds. This is part of a joint project with Felix Thimm dedicated to the proof of the GW/PT-correspondence for Calabi-Yau $4$-folds by implementing Pardon's programme in dimension $4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03566",
  "author_total": 1,
  "authors": [
    {
      "name": "Ivan Karpov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aqaf9xkp7qgqb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03566",
  "fulltext_url": null,
  "id": "aqaf9xkp7qgqb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03566",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03566",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aqaf9xkp7qgqb.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03566",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03566"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "GW/PT-correspondence for CY $4$-fold-II: Virtual Classes",
  "title_text": "GW/PT-correspondence for CY $4$-fold-II: Virtual Classes",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/aqaf9xkp7qgqb",
  "venue": "arXiv",
  "versions": []
}