{
  "id": "1710.10152",
  "version": "v1",
  "published": "2017-10-27T14:20:37.000Z",
  "updated": "2017-10-27T14:20:37.000Z",
  "title": "Very stable bundles and properness of the Hitchin map",
  "authors": [
    "Christian Pauly",
    "Ana Peón-Nieto"
  ],
  "comment": "5 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a smooth complex projective curve of genus $g\\geq 2$ and let $K$ be its canonical bundle. In this note we show that a stable vector bundle $E$ on $X$ is very stable, i.e. $E$ has no non-zero nilpotent Higgs field, if and only if the restriction of the Hitchin map to the vector space of Higgs fields $H^0(X, \\mathrm{End}(E) \\otimes K)$ is a proper map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-27T14:20:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "14H70"
    ],
    "keywords": [
      "hitchin map",
      "stable bundles",
      "properness",
      "non-zero nilpotent higgs field",
      "smooth complex projective curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}