{
  "id": "math/9903162",
  "version": "v3",
  "published": "1999-03-28T19:47:33.000Z",
  "updated": "1999-10-06T19:00:20.000Z",
  "title": "Essential dimensions of algebraic groups and a resolution theorem for G-varieties",
  "authors": [
    "Zinovy Reichstein",
    "Boris Youssin",
    "János Kollár",
    "Endre Szabó"
  ],
  "comment": "This revision contains new lower bounds for essential dimensions of algebraic groups of types A_n and E_7. AMS LaTeX 1.1, 42 pages. Paper by Zinovy Reichstein and Boris Youssi, includes an appendix by J\\'anos Koll\\'ar and Endre Szab\\'o. Author-supplied dvi file available at http://ucs.orst.edu/~reichstz/pub.html",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let G be an algebraic group and let X be a generically free G-variety. We show that X can be transformed, by a sequence of blowups with smooth G-equivariant centers, into a G-variety X' with the following property: the stabilizer of every point of X' is isomorphic to a semidirect product of a unipotent group U and a diagonalizable group A. As an application of this and related results, we prove new lower bounds on essential dimensions of some algebraic groups. We also show that certain polynomials in one variable cannot be simplified by a Tschirnhaus transformation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1999-10-06T19:00:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic group",
      "essential dimensions",
      "resolution theorem",
      "smooth g-equivariant centers",
      "tschirnhaus transformation"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......3162R"
    }
  }
}