{
  "id": "math/0403033",
  "version": "v2",
  "published": "2004-03-02T04:24:50.000Z",
  "updated": "2004-03-06T01:08:36.000Z",
  "title": "Vanishing of the top Chern classes of the moduli of vector bundles",
  "authors": [
    "Young-Hoon Kiem",
    "Jun Li"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $Y$ be a smooth projective curve of genus $g\\ge 2$ and let $M_{r,d}(Y)$ be the moduli space of stable vector bundles of rank $r$ and degree $d$ on $Y$. A classical conjecture of Newstead and Ramanan states that $ c_i(M_{2,1}(Y))=0$ for $i>2(g-1)$ i.e. the top $2g-1$ Chern classes vanish. The purpose of this paper is to generalize this vanishing result to the rank 3 case by generalizing Gieseker's degeneration method. More precisely, we prove that $c_i(M_{3,1}(Y))=0$ for $i>6g-5$. In other words, the top $3g-3$ Chern classes vanish. Notice that we also have $c_i(M_{3,2}(Y))=0$ for $i>6g-5$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-03-06T01:08:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "14F25",
      "14F42"
    ],
    "keywords": [
      "chern classes vanish",
      "generalizing giesekers degeneration method",
      "smooth projective curve",
      "stable vector bundles",
      "moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3033K"
    }
  }
}