{
  "id": "math/9808029",
  "version": "v4",
  "published": "1998-08-06T02:43:45.000Z",
  "updated": "2000-07-01T00:00:00.000Z",
  "title": "The quantization conjecture revisited",
  "authors": [
    "Constantin Teleman"
  ],
  "comment": "43 pages, published version",
  "journal": "Ann. of Math. (2) 152 (2000), no. 1, 1-43",
  "categories": [
    "math.AG",
    "math.SG"
  ],
  "abstract": "A strong version of the quantization conjecture of Guillemin and Sternberg is proved. For a reductive group action on a smooth, compact, polarized variety (X,L), the cohomologies of L over the GIT quotient X // G equal the invariant part of the cohomologies over X. This generalizes the theorem of [Invent. Math. 67 (1982), 515-538] on global sections, and strengthens its subsequent extensions to Riemann-Roch numbers. Remarkable by-products are the invariance of cohomology of vector bundles over X // G under a small change in the defining polarization or under shift desingularization, as well as a new proof of Boutot's theorem. Also studied are equivariant holomorphic forms and the equivariant Hodge-to-de Rham spectral sequences for X and its strata, whose collapse is shown. One application is a new proof of the Borel-Weil-Bott theorem of [Invent. Math. 134 (1998), 1-57] for the moduli stack of G-bundles over a curve, and of analogous statements for the moduli stacks and spaces of bundles with parabolic structures. Collapse of the Hodge-to-de Rham sequences for these stacks is also shown.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2000-07-01T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantization conjecture",
      "equivariant hodge-to-de rham spectral sequences",
      "moduli stack",
      "hodge-to-de rham sequences",
      "equivariant holomorphic forms"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......8029T"
    }
  }
}