{
  "id": "2002.00358",
  "version": "v1",
  "published": "2020-02-02T10:14:04.000Z",
  "updated": "2020-02-02T10:14:04.000Z",
  "title": "On the Moduli space of $λ$-connections",
  "authors": [
    "Anoop Singh"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a compact Riemann surface of genus $g \\geq 3$. Let $\\cat{M}_{Hod}$ denote the moduli space of stable $\\lambda$-connections over $X $ and $\\cat{M}'_{Hod} \\subset \\cat{M}_{Hod}$ denote the subvariety whose underlying vector bundle is stable. Fix a line bundle $L$ of degree zero. Let $\\cat{M}_{Hod}(L)$ denote the moduli space of stable $\\lambda$-connections with fixed determinant $L$ and $\\cat{M}'_{Hod}(L) \\subset \\cat{M}_{Hod}(L)$ be the subvariety whose underlying vector bundle is stable. We show that there is a natural compactification of $\\cat{M}'_{Hod}$ and $\\cat{M}'_{Hod} (L)$, and study their Picard groups. Let $\\M_{Hod}(L)$ denote the moduli space of polystable $\\lambda$-connections. We investigate the nature of algebraic functions on $\\cat{M}_{Hod}(L)$ and $\\M_{Hod}(L)$. We also study the automorphism group of $\\cat{M}'_{Hod}(L)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-02T10:14:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14C22",
      "14E05",
      "14J50"
    ],
    "keywords": [
      "moduli space",
      "connections",
      "vector bundle",
      "compact riemann surface",
      "picard groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}