{
  "abstract": "Let $X$ be a product-quotient surface, which is by definition a minimal resolution of $(C_1\\times C_2)/G$, where $C_i$ are smooth curves of genus $\\geq 2$ and $G$ is a finite group. When $G$ acts freely, we show that every product Bridgeland stability condition on $C_1\\times C_2$ induces a tilt stability condition on $X$, and that, if $p_g(X)=q(X)=0$, every tilt stability condition on $X$ arises this way. When $(C_1\\times C_2)/G$ has only $A_1$-singularities, we use induction \\cite{MMS} and derived McKay correspondence \\cite{BKR} to produce non-geometric stability conditions $σ_X$ on $X$, which satisfy the full support property and lie in the closure of the geometric chamber. Whether $σ_X$ also lies in the closure of the $\\widetilde{\\mathrm{GL}}^+(2,\\mathbb{R})$-orbit of the tilt stability conditions depends on a single inequality, $ω_X^2 \\ge n/8$, where $n$ is the number of $A_1$-singularities. When it fails, the geometric chamber is strictly larger than this orbit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15276",
  "author_total": 1,
  "authors": [
    {
      "name": "Uttaran Dutta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/25jqbyws717t5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15276",
  "fulltext_url": null,
  "id": "25jqbyws717t5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15276",
  "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": "W7221797515",
  "pdf_url": "https://arxiv.org/pdf/2610.15276",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/25jqbyws717t5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15276",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15276"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A note on stability conditions on product-quotient surfaces",
  "title_text": "A note on stability conditions on product-quotient surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/25jqbyws717t5",
  "venue": "arXiv",
  "versions": []
}