{
  "id": "math/0607663",
  "version": "v1",
  "published": "2006-07-26T10:38:00.000Z",
  "updated": "2006-07-26T10:38:00.000Z",
  "title": "On the fundamental group of real toric varieties",
  "authors": [
    "V Uma"
  ],
  "comment": "17 pages",
  "journal": "Proc. Indian Acad. Sci. (Math. Sci), Vol. 114, No. 1, February 2004, pp-15-31.",
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "Let $X(\\Delta)$ be the real toric variety associated to a smooth fan $\\Delta$. The main purpose of this article is: (i) to determine the fundamental group and the universal cover of $X(\\Delta)$, (ii) to give necessary and sufficient conditions on $\\Delta$ under which $\\pi_1(X(\\Delta))$ is abelian, (iii) to give necessary and sufficient conditions on $\\Delta$ under which $X(\\Delta)$ is aspherical, and when $\\Delta$ is complete, (iv) to give necessary and sufficient conditions for $\\cc_{\\Delta}$ to be a $K(\\pi,1)$ space where $\\cc_{\\Delta}$ is the complement of a real subspace arrangement associated to $\\Delta$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-26T10:38:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fundamental group",
      "sufficient conditions",
      "real toric variety",
      "universal cover",
      "smooth fan"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7663U"
    }
  }
}