{
  "id": "0910.0120",
  "version": "v1",
  "published": "2009-10-01T09:36:52.000Z",
  "updated": "2009-10-01T09:36:52.000Z",
  "title": "Inversion of series and the cohomology of the moduli spaces $\\mathcal{M}^δ_{0,n}$",
  "authors": [
    "Francis Brown",
    "Jonas Bergström"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "For $n\\geq 3$, let $\\mathcal{M}_{0,n}$ denote the moduli space of genus 0 curves with $n$ marked points, and $\\overline{\\mathcal{M}}_{0,n}$ its smooth compactification. A theorem due to Ginzburg, Kapranov and Getzler states that the inverse of the exponential generating series for the Poincar\\'e polynomial of $H^{\\bullet}(\\mathcal{M}_{0,n})$ is given by the corresponding series for $H^{\\bullet}(\\overline{\\mathcal{M}}_{0,n})$. In this paper, we prove that the inverse of the ordinary generating series for the Poincar\\'e polynomial of $H^{\\bullet}(\\mathcal{M}_{0,n})$ is given by the corresponding series for $H^{\\bullet}(\\mathcal{M}^{\\delta}_{0,n})$, where $\\mathcal{M}_{0,n}\\subset \\mathcal{M}^{\\delta}_{0,n} \\subset \\overline{\\mathcal{M}}_{0,n}$ is a certain smooth affine scheme.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-01T09:36:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10"
    ],
    "keywords": [
      "moduli space",
      "cohomology",
      "poincare polynomial",
      "smooth affine scheme",
      "corresponding series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.0120B"
    }
  }
}