{
  "abstract": "We classify all open substacks admitting a proper good moduli space inside the stack $\\mathcal{G}_{1,n}$ of log-canonically polarized Gorenstein curves of genus one with $n$ distinct marked points: they are exactly the stacks $\\overline{\\mathcal{M}}_{1,n}(c)$ defined by Bozlee--Kuo--Neff. Restricting to the case where $c$ is pure of level $m$, we then give a numerical criterion for the projectivity of the good moduli spaces: these turn out to be asymptotically almost never projective as $n$ tends to infinity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08742",
  "author_total": 3,
  "authors": [
    {
      "name": "Luca Battistella"
    },
    {
      "name": "Andrea Di Lorenzo"
    },
    {
      "name": "Michele Pernice"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/72d341nes8ebq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08742",
  "fulltext_url": null,
  "id": "72d341nes8ebq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08742",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7220965578",
  "pdf_url": "https://arxiv.org/pdf/2610.08742",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/72d341nes8ebq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08742",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08742"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The unbearable projectivity of being a good moduli space of Gorenstein curves of genus one with non-colliding markings",
  "title_text": "The unbearable projectivity of being a good moduli space of Gorenstein curves of genus one with non-colliding markings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/72d341nes8ebq",
  "venue": "arXiv",
  "versions": []
}