{
  "abstract": "A general $4\\times3\\times3$ tensor defines three determinantal varieties in $\\mathbb{P}^3$ and $\\mathbb{P}^2$ and $\\mathbb{P}^2$ where it drops rank: a cubic surface and two length 6 subschemes. We study the Geometric Invariant Theory (GIT) quotient of $\\mathbb{P}(\\mathbb{C}^4\\otimes\\mathbb{C}^3\\otimes\\mathbb{C}^3)$ by $\\operatorname{SL}(4)\\times\\operatorname{SL}(3)\\times\\operatorname{SL}(3)$, a moduli space of linear determinantal representations of cubic surfaces. We give a geometric description of the (semi)stable locus and some of the geometry of this GIT quotient. This GIT quotient admits a surjective rational map to the GIT moduli space of cubic surfaces, undefined at only one point.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28497",
  "author_total": 1,
  "authors": [
    {
      "name": "Charlotte Sherratt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/91h5jzhz5p791.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28497",
  "fulltext_url": null,
  "id": "91h5jzhz5p791",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28497",
  "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": "W7214300455",
  "pdf_url": "https://arxiv.org/pdf/2609.28497",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/91h5jzhz5p791.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28497",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28497"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The GIT of 4x3x3 tensors (determinantal cubic surfaces)",
  "title_text": "The GIT of 4x3x3 tensors (determinantal cubic surfaces)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/91h5jzhz5p791",
  "venue": "arXiv",
  "versions": []
}