{
  "id": "1402.5096",
  "version": "v1",
  "published": "2014-02-20T18:40:10.000Z",
  "updated": "2014-02-20T18:40:10.000Z",
  "title": "On the equations and classification of toric quiver varieties",
  "authors": [
    "M. Domokos",
    "Dániel Joó"
  ],
  "categories": [
    "math.RT",
    "math.AC",
    "math.AG"
  ],
  "abstract": "Toric quiver varieties (moduli spaces of quiver representations) are studied. Given a quiver and a weight there is an associated quasiprojective toric variety together with a canonical embedding into projective space. It is shown that for a quiver with no oriented cycles the homogeneous ideal of this embedded projective variety is generated by elements of degree at most $3$. In each fixed dimension $d$ up to isomorphism there are only finitely many $d$-dimensional toric quiver varieties. A procedure for their classification is outlined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-20T18:40:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "14L24",
      "16G20",
      "52B20"
    ],
    "keywords": [
      "classification",
      "dimensional toric quiver varieties",
      "quiver representations",
      "moduli spaces",
      "associated quasiprojective toric variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.5096D"
    }
  }
}