{
  "id": "1907.13431",
  "version": "v1",
  "published": "2019-07-31T11:53:44.000Z",
  "updated": "2019-07-31T11:53:44.000Z",
  "title": "Chow Group of 1-cycles of the Moduli of Parabolic Bundles of Rank 2 Over a Curve",
  "authors": [
    "Sujoy Chakraborty"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let us fix a nonsingular projective curve $X$ of genus $g\\geq 3$ over $\\mathbb{C}$, and choose a point $x\\in X$. Let $\\mathcal{M}$ denote the moduli space of isomorphism classes of stable vector bundles of rank 2 and fixed determinant $\\mathcal{O}_X(x)$ over $X$. Let us moreover fix $n$ distinct closed points $S=\\{p_1,p_2,..., p_n\\}$ over $X$, referred to as $\\textit{parabolic points}$, and parabolic weights $(\\alpha):= 0\\leq \\alpha_1 <\\alpha_2<1 $ over the parabolic points. We also assume that the weights are generic. Let $\\mathcal{M}_\\alpha$ denote the moduli space of $S$-equivalence classes of parabolic stable vector bundles of rank 2 over $X$ of fixed determinant $\\mathcal{O}_X(x)$. The Chow groups of these moduli spaces are interesting objects to study. I. Choe and J. Hwang showed that there is a canonical isomorphism $CH_1^{\\mathbb{Q}}(\\mathcal{M}) \\cong CH_0^{\\mathbb{Q}}(X)$. Here our aim is to find $CH_1^{\\mathbb{Q}}(\\mathcal{M}_{\\alpha})$ for generic weights $\\alpha$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-31T11:53:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C15",
      "14D20",
      "14D22"
    ],
    "keywords": [
      "chow group",
      "parabolic bundles",
      "moduli space",
      "parabolic stable vector bundles",
      "fixed determinant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}