{
  "id": "2009.14680",
  "version": "v1",
  "published": "2020-09-30T13:55:29.000Z",
  "updated": "2020-09-30T13:55:29.000Z",
  "title": "An Analytic Approach to the Quasi-projectivity of the Moduli Space of Higgs Bundles",
  "authors": [
    "Yue Fan"
  ],
  "comment": "26 pages",
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "The moduli space of Higgs bundles can be defined as a quotient of an infinite-dimensional space. Moreover, by the Kuranishi slice method, it is equipped with the structure of a normal complex space. In this paper, we will use analytic methods to show that the moduli space is quasi-projective. In fact, following Hausel's method, we will use the symplectic cut to construct a normal and projective compactification of the moduli space, and hence prove the quasi-projectivity. The main difference between this paper and Hausel's is that the smoothness of the moduli space is not assumed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-30T13:55:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "higgs bundles",
      "analytic approach",
      "quasi-projectivity",
      "kuranishi slice method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}