{
  "id": "0706.4353",
  "version": "v2",
  "published": "2007-06-29T13:08:28.000Z",
  "updated": "2008-06-13T10:28:19.000Z",
  "title": "Geometric Invariant Theory via Cox Rings",
  "authors": [
    "Ivan V. Arzhantsev",
    "Juergen Hausen"
  ],
  "comment": "27 pages, minor changes, Example 8.8 replaced, to appear in Journal of Pure and Applied Algebra",
  "journal": "J. Pure Appl. Algebra 213, 154-172 (2009)",
  "categories": [
    "math.AG"
  ],
  "abstract": "We consider actions of reductive groups on a varieties with finitely generated Cox ring, e.g., the classical case of a diagonal action on a product of projective spaces. Given such an action, we construct via combinatorial data in the Cox ring all maximal open subsets such that the quotient is quasiprojective or embeddable into a toric variety. As applications, we obtain an explicit description of the chamber structure of the linearized ample cone and several Gelfand-MacPherson type correspondences relating quotients of reductive groups to quotients of torus actions. Moreover, our approach provides information on the geometry of many of the resulting quotient spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-06-13T10:28:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L24",
      "14L30",
      "14C20"
    ],
    "keywords": [
      "geometric invariant theory",
      "cox ring",
      "gelfand-macpherson type correspondences relating quotients",
      "maximal open subsets",
      "reductive groups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.4353A"
    }
  }
}