{
  "abstract": "We develop Geometric Invariant Theory for affine superschemes under the action of reductive algebraic supergroups, formulating the theory in terms of coordinate Hopf superalgebras in order to accommodate anticommuting and nilpotent variables. Within this algebraic setting, we construct affine superquotients and establish their basic structural properties under suitable hypotheses. We then prove a supergeometric analogue of the Hilbert-Mumford criterion, giving a numerical test for the semistability and stability of points under natural constraints on the supergroup coaction. We show that this numerical criterion can be used to construct the GIT superquotient of these superschemes, and we give examples illustrating how the supergeometric GIT superquotient differs from its classical counterpart.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14904",
  "author_total": 3,
  "authors": [
    {
      "name": "Alexander Quintero Velez"
    },
    {
      "name": "Pedro Rizzo"
    },
    {
      "name": "Alexander Torres-Gomez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8dxek5wt95g7m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14904",
  "fulltext_url": null,
  "id": "8dxek5wt95g7m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14904",
  "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",
      "hep-th"
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      "arxiv",
      "math-ph"
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      "arxiv",
      "math.AG"
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      "arxiv",
      "math.MP"
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      "arxiv",
      "math.RT"
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    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
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  "openalex": "W7213295390",
  "pdf_url": "https://arxiv.org/pdf/2609.14904",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8dxek5wt95g7m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14904",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14904"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Geometric Invariant Theory for Affine Superschemes",
  "title_text": "Geometric Invariant Theory for Affine Superschemes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/8dxek5wt95g7m",
  "venue": "arXiv",
  "versions": []
}