{
  "abstract": "We construct a bubble-tree enhancement of the KSBA moduli space of surfaces of general type using index-one-cover Deligne--Mumford stacks. The construction is inspired by bubbling phenomena for Kähler--Einstein metrics. Non-klt semi-log-canonical singularities are replaced by admissible simple-normal-crossing configurations: the cusp and degenerate-cusp components are rational, while the simple-elliptic case also contains elliptic ruled components. A key feature is that the construction avoids lci covers. We construct the moduli stack of polarized bubble-tree index-one-cover Deligne-Mumford stacks. The stack is in general not separated, and we construct its underlying separated algebraic space. We also construct the moduli stack of bubble-tree index-one-cover Deligne-Mumford stacks with labeled sections that record algebraic bubbling centers and compare it with the pointed metric bubble tree. The labeled sections determine a numerical class whose stability proves the separatedness of the moduli stack. We establish a perfect obstruction theory and a virtual fundamental class on the bubble-tree moduli stacks. This provides a novel and geometric pathway to prove the existence of a virtual fundamental class on the original KSBA moduli space, thus offering a new approach to a conjecture of Donaldson. We expect that parts of the construction extend to higher dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04154",
  "author_total": 1,
  "authors": [
    {
      "name": "Yunfeng Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/66n8z0vrcsshz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04154",
  "fulltext_url": null,
  "id": "66n8z0vrcsshz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04154",
  "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/2611.04154",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/66n8z0vrcsshz.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04154",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04154"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Bubble Compactification of KSBA Moduli Space of Surfaces of General Type",
  "title_text": "A Bubble Compactification of KSBA Moduli Space of Surfaces of General Type",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/66n8z0vrcsshz",
  "venue": "arXiv",
  "versions": []
}