{
  "id": "math/9810116",
  "version": "v1",
  "published": "1998-10-19T02:00:13.000Z",
  "updated": "1998-10-19T02:00:13.000Z",
  "title": "Omega Admissible Theory II: New metrics on determinant of cohomology And Their applications to moduli spaces of punctured Riemann surfaces",
  "authors": [
    "Lin Weng"
  ],
  "comment": "AMS-TEX",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "For singular metrics, there is no Quillen metric formalism on cohomology determinant. In this paper, we develop an admissible theory, with which the arithmetic Deligne-Riemann-Roch isometry can be established for singular metrics. As an application, we first study Weil-Petersson metrics and Takhtajan-Zograf metrics on moduli spaces of punctured Riemann surfaces, and then give a more geometric interpretation of our determinant metrics in terms of Selberg zeta functions. We end this paper by proposing an arithmetic factorization for Weil-Petersson metrics, cuspidal metrics and Selberg zeta functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-10-19T02:00:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "punctured riemann surfaces",
      "omega admissible theory",
      "moduli spaces",
      "determinant",
      "selberg zeta functions"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....10116W"
    }
  }
}