{
  "id": "1012.5541",
  "version": "v3",
  "published": "2010-12-26T19:28:36.000Z",
  "updated": "2012-02-03T19:03:02.000Z",
  "title": "The singular fibre of the Hitchin map",
  "authors": [
    "Peter B. Gothen",
    "André Oliveira"
  ],
  "comment": "28 pages; v3; minor changes: added Proposition 3.7 and main Theorem 8.1 now also refers the fibre over zero; final version",
  "doi": "10.1093/imrn/rns020",
  "categories": [
    "math.AG"
  ],
  "abstract": "Given any line bundle L of positive degree, on a compact Riemann surface, let $M_L^\\Lambda$ be the moduli space of L-twisted Higgs pairs of rank 2 with fixed determinant isomorphic to $\\Lambda$ and traceless Higgs field. We give a description of the singular fibre of the Hitchin map $H:M^L_\\Lambda\\to H^0(L^2)$, when the corresponding spectral curve has any singularity of type $A_{m-1}$. In particular, we prove directly that this fibre is connected.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-02-03T19:03:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "14H40"
    ],
    "keywords": [
      "hitchin map",
      "singular fibre",
      "compact riemann surface",
      "line bundle",
      "corresponding spectral curve"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.5541G"
    }
  }
}