{
  "id": "1202.5760",
  "version": "v3",
  "published": "2012-02-26T14:24:10.000Z",
  "updated": "2013-02-02T20:11:27.000Z",
  "title": "Quotients of an affine variety by an action of a torus",
  "authors": [
    "Olga V. Chuvashova",
    "Nikolay A. Pechenkin"
  ],
  "comment": "21 pages",
  "journal": "Central European Journal of Mathematics 11 (2013), no.11, 1863-1880",
  "doi": "10.2478/s11533-013-0295-8",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be an affine T-variety. We study two different quotients for the action of T on X: the toric Chow quotient X/_CT and the toric Hilbert scheme H. We introduce a notion of the main component H_0 of H which parameterizes general T-orbit closures in X and their flat limits. The main component U_0 of the universal family U over H is a preimage of H_0. We define an analogue of a universal family W_X over the main component of the X/_CT. We show that the toric Chow morphism restricted on the main components lifts to a birational projective morphism from U_0 to W_X. The variety W_X also provides a geometric realization of the Altmann-Hausen family. In particular, the notion of W_X allows us to provide an explicit description of the fan of the Altmann-Hausen family in the toric case.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-02-02T20:11:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L24",
      "14C05",
      "14M25"
    ],
    "keywords": [
      "affine variety",
      "parameterizes general t-orbit closures",
      "toric hilbert scheme",
      "toric chow quotient",
      "toric chow morphism"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.5760C"
    }
  }
}