{
  "id": "2310.20709",
  "version": "v1",
  "published": "2023-10-31T17:59:58.000Z",
  "updated": "2023-10-31T17:59:58.000Z",
  "title": "Quadratic Differentials as Stability Conditions of Graded Skew-gentle Algebras",
  "authors": [
    "Suiqi Lu",
    "Yu Qiu",
    "Dongjian Wu"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We prove that the principal component of the exchange graph of hearts of a graded skew-gentle algebra can be identified with the corresponding exchange graph of S-graphs, using the geometric models and $\\operatorname{Int}=\\operatorname{dim}\\operatorname{Hom}$ formula in Qiu-Zhang-Zhou. Using the same argument in Bridgeland-Smith, Barbieri-M\\\"oller-Qiu-So and Christ-Haiden-Qiu, we extend this identification to an isomorphism between the spaces of stability conditions and of quadratic differentials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-31T17:59:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "graded skew-gentle algebra",
      "stability conditions",
      "quadratic differentials",
      "geometric models",
      "corresponding exchange graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}