{
  "id": "math/0510088",
  "version": "v2",
  "published": "2005-10-05T11:51:19.000Z",
  "updated": "2005-10-14T12:55:24.000Z",
  "title": "Geometry of $B \\times B$-orbit closures in equivariant embeddings",
  "authors": [
    "Xuhua He",
    "Jesper Funch Thomsen"
  ],
  "comment": "23 pages, revised version. Minor problem with definition of $\\mathcal I$ in Section 5.3 resolved",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ denote an equivariant embedding of a connected reductive group $G$ over an algebraically closed field $k$. Let $B$ denote a Borel subgroup of $G$ and let $Z$ denote a $B \\times B$-orbit closure in $X$. When the characteristic of $k$ is positive and $X$ is projective we prove that $Z$ is globally $F$-regular. As a consequence, $Z$ is normal and Cohen-Macaulay for arbitrary $X$ and arbitrary characteristics. Moreover, in characteristic zero it follows that $Z$ has rational singularities. This extends earlier results by the second author and M. Brion.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-10-14T12:55:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M17",
      "14L30",
      "14B05"
    ],
    "keywords": [
      "orbit closure",
      "equivariant embedding",
      "extends earlier results",
      "characteristic zero",
      "arbitrary characteristics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10088H"
    }
  }
}