{
  "id": "1207.6941",
  "version": "v3",
  "published": "2012-07-30T14:00:26.000Z",
  "updated": "2014-10-21T16:06:56.000Z",
  "title": "Singularity categories of gentle algebras",
  "authors": [
    "Martin Kalck"
  ],
  "comment": "11 pages; minor changes, final version, to appear Bulletin of the LMS",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We determine the singularity category of an arbitrary finite dimensional gentle algebra $\\Lambda$. It is a finite product of $n$-cluster categories of type $\\mathbb{A}_{1}$. Equivalently, it may be described as the stable module category of a selfinjective gentle algebra. If $\\Lambda$ is a Jacobian algebra arising from a triangulation $\\ct$ of an unpunctured marked Riemann surface, then the number of factors equals the number of inner triangles of $\\ct$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-16T16:12:55.000Z",
      "abstract": "We determine the singularity category of an arbitrary finite dimensional gentle algebra $\\Lambda$. It is a finite product of $n$-cluster categories of type $\\mathbb{A}_{1}$. If $\\Lambda$ is a Jacobian algebra arising from a triangulation $\\ct$ of an unpunctured marked Riemann surface, then the number of factors equals the number of inner triangles of $\\ct$.",
      "comment": "10 pages; major changes: corrected a wrong argument in Subsection 4.1 - the results hold without changes; corollary on derived invariants added; added some examples and remarks; exposition clarified; introduction extended",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-21T16:06:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "16G20"
    ],
    "keywords": [
      "singularity category",
      "arbitrary finite dimensional gentle algebra",
      "inner triangles",
      "finite product",
      "jacobian algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.6941K"
    }
  }
}