{
  "id": "math/9811053",
  "version": "v1",
  "published": "1998-11-09T09:42:37.000Z",
  "updated": "1998-11-09T09:42:37.000Z",
  "title": "The GIT-equivalence for $G$-line bundles",
  "authors": [
    "Nicolas Ressayre"
  ],
  "comment": "36 pages, 4 figures",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a projective variety with an action of a reductive group $G$. Each ample $G$-line bundle $L$ on $X$ defines an open subset $X^{\\rm ss}(L)$ of semi-stable points. Following Dolgachev and Hu, define a GIT-class as the set of algebraic equivalence classes of $L'$s with fixed $X^{\\rm ss}(L)$. We show that the GIT-classes are the relative interiors of rational polyhedral convex cones, which form a fan in the $G$-ample cone. We also study the corresponding variations of quotients $X^{\\rm ss}(L)//G$. This sharpens results of Thaddeus and Dolgachev-Hu.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-11-09T09:42:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "line bundle",
      "git-equivalence",
      "rational polyhedral convex cones",
      "algebraic equivalence classes",
      "open subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....11053R"
    }
  }
}