{
  "id": "1707.00834",
  "version": "v1",
  "published": "2017-07-04T07:27:43.000Z",
  "updated": "2017-07-04T07:27:43.000Z",
  "title": "The minimal model program for b-log canonical divisors and applications",
  "authors": [
    "Daniel Chan",
    "Kenneth Chan",
    "Louis de Thanhoffer de Völcsey",
    "Colin Ingalls",
    "Kelly Jabbusch",
    "Sándor J Kovács",
    "Rajesh Kulkarni",
    "Boris Lerner",
    "Basil Nanayakkara",
    "Shinnosuke Okawa",
    "Michel Van den Berg"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We discuss the minimal model program for b-log varieties, which is a pair of a variety and a b-divisor, as a natural generalization of the minimal model program for ordinary log varieties. We show that the main theorems of the log MMP work in the setting of the b-log MMP. If we assume that the log MMP terminates, then so does the b- log MMP. Furthermore, the b-log MMP includes both the log MMP and the equivariant MMP as special cases. There are various interesting b-log varieties arising from different objects, including the Brauer pairs, or \"non-commutative algebraic varieties which are finite over their centres\". The case of toric Brauer pairs is discussed in further detail.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-04T07:27:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E30",
      "14A22"
    ],
    "keywords": [
      "minimal model program",
      "b-log canonical divisors",
      "b-log varieties",
      "b-log mmp",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}