{
  "id": "math/9902003",
  "version": "v1",
  "published": "1999-02-01T11:12:14.000Z",
  "updated": "1999-02-01T11:12:14.000Z",
  "title": "The Mixed Hodge Structure on the Fundamental Group of a Punctured Riemann Surface",
  "authors": [
    "Rainer H. Kaenders"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Given a compact Riemann surface $\\bar{X}$ of genus $g$ and a point $q$ on $\\bar{X}$, we consider $X:=\\bar{X}\\setminus\\{q\\}$ with a basepoint $p\\in X$. The extension of mixed Hodge structures, given by the weights -1 and -2, of the mixed Hodge structure on the fundamental group (in the sense of Hain) is studied. We show that it naturally corresponds on the one hand to the element $(2g q-2 p-K)$ in $\\Pic^0(\\bar{X})$, where $K$ represents the canonical divisor, and on the other hand to the respective extension of $\\bar{X}$. Finally, we prove a pointed Torelli theorem for punctured Riemann surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-02-01T11:12:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H40",
      "14H30",
      "14F35"
    ],
    "keywords": [
      "mixed hodge structure",
      "punctured riemann surface",
      "fundamental group",
      "compact riemann surface",
      "pointed torelli theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......2003K"
    }
  }
}