{
  "id": "math/0404351",
  "version": "v1",
  "published": "2004-04-20T02:51:46.000Z",
  "updated": "2004-04-20T02:51:46.000Z",
  "title": "Cohomology of the moduli space of Hecke cycles",
  "authors": [
    "Insong Choe",
    "Jaeyoo Choy",
    "Young-Hoon Kiem"
  ],
  "comment": "22 pages, 1 figure",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a smooth projective curve of genus $g \\ge 3$ and let $M_0$ be the moduli space of semistable bundles over $X$ of rank 2 with trivial determinant. Three different desingularizations of $M_0$ have been constructed by Seshadri \\cite{Se1}, Narasimhan-Ramanan \\cite{NR}, and Kirwan \\cite{k5}. In this paper, we construct a birational morphism from Kirwan's desingularization to Narasimhan-Ramanan's, and prove that the Narasimhan-Ramanan's desingularization (called the moduli space of Hecke cycles) is the intermediate variety between Kirwan's and Seshadri's as was conjectured recently in \\cite{KL}. As a by-product, we compute the cohomology of the moduli space of Hecke cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-20T02:51:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "14F25",
      "14F42"
    ],
    "keywords": [
      "moduli space",
      "hecke cycles",
      "cohomology",
      "trivial determinant",
      "kirwans desingularization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4351C"
    }
  }
}