{
  "abstract": "We construct a compactification P Ξ M ¯ g , n ( μ ) \\mathbb {P}\\Xi \\overline {\\mathcal {M}}_{g,n}(\\mu ) of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles. This compactification, called the moduli space of multi-scale differentials, is a complex orbifold with normal crossing boundary. Locally, P Ξ M ¯ g , n ( μ ) \\mathbb {P}\\Xi \\overline {\\mathcal {M}}_{g,n}(\\mu ) can be described as the normalization of an explicit blowup of the incidence variety compactification, which was defined by Bainbridge, Chen, Gendron, Grushevsky, and Möller [Duke Math. J. 167 (2018), pp. 2347–2416] as the closure of the stratum of abelian differentials in the closure of the Hodge bundle. We also define families of projectivized multi-scale differentials, which gives a proper smooth Deligne-Mumford stack, and P Ξ M ¯ g , n ( μ ) \\mathbb {P}\\Xi \\overline {\\mathcal {M}}_{g,n}(\\mu ) is the orbifold corresponding to it. Moreover, we perform a real oriented blowup of the unprojectivized space Ξ M ¯ g , n ( μ ) \\Xi \\overline {\\mathcal {M}}_{g,n}(\\mu ) such that the G L 2 + (",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "name": "Matt Bainbridge",
      "orcid": "0009-0002-7992-8209"
    },
    {
      "name": "Dawei Chen",
      "orcid": "0000-0002-3926-2636"
    },
    {
      "name": "Quentin Gendron"
    },
    {
      "name": "Samuel Grushevsky",
      "orcid": "0000-0002-9943-3804"
    },
    {
      "name": "Martin Möller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6nx57r9a16rze.bib",
  "cited_by": 82,
  "doi": "10.1090/cams/78",
  "fulltext_url": null,
  "id": "6nx57r9a16rze",
  "issns": [
    "2692-3688"
  ],
  "landing_url": "https://doi.org/10.1090/cams/78",
  "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": [
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W2982288791",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": "American Mathematical Society",
  "ris": "https://research.draconitic.com/paper/6nx57r9a16rze.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W2982288791",
      "source": "openalex",
      "url": "https://doi.org/10.1090/cams/78"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic Geometry and Number Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The moduli space of multi-scale differentials",
  "title_text": "The moduli space of multi-scale differentials",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:20:59Z",
  "url": "https://research.draconitic.com/paper/6nx57r9a16rze",
  "venue": "Communications of the American Mathematical Society",
  "versions": []
}