{
  "abstract": "We determine the intrinsic mirror of an orbifold cubic surface with three nodes and interpret the resulting geometry through mirror symmetry between the $PGL(2,\\mathbb{C})$ and $SL(2,\\mathbb{C})$ character varieties of the once-punctured torus. We further construct a quantization of the mirror using higher genus Gromov-Witten theory and show that it recovers the $A_1$ spherical double affine Hecke algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38556",
  "author_total": 2,
  "authors": [
    {
      "name": "Pierrick Bousseau"
    },
    {
      "name": "Sayan Chattopadhyay"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fsbv35ghdeagd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38556",
  "fulltext_url": null,
  "id": "fsbv35ghdeagd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38556",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  ],
  "openalex": "W7215083587",
  "pdf_url": "https://arxiv.org/pdf/2609.38556",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fsbv35ghdeagd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.38556",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38556"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Intrinsic mirror symmetry for orbifold cubic surfaces and the $A_1$ spherical DAHA",
  "title_text": "Intrinsic mirror symmetry for orbifold cubic surfaces and the A_1 spherical DAHA",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/fsbv35ghdeagd",
  "venue": "arXiv",
  "versions": []
}