{
  "id": "math/9204225",
  "version": "v1",
  "published": "1992-04-01T00:00:00.000Z",
  "updated": "1992-04-01T00:00:00.000Z",
  "title": "Higgs line bundles, Green-Lazarsfeld sets,and maps of Kähler manifolds to curves",
  "authors": [
    "Donu Arapura"
  ],
  "comment": "5 pages",
  "journal": "Bull. Amer. Math. Soc. (N.S.) 26 (1992) 310-314",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a compact K\\\"ahler manifold. The set $\\cha(X)$ of one-dimensional complex valued characters of the fundamental group of $X$ forms an algebraic group. Consider the subset of $\\cha(X)$ consisting of those characters for which the corresponding local system has nontrivial cohomology in a given degree $d$. This set is shown to be a union of finitely many components that are translates of algebraic subgroups of $\\cha(X)$. When the degree $d$ equals 1, it is shown that some of these components are pullbacks of the character varieties of curves under holomorphic maps. As a corollary, it is shown that the number of equivalence classes (under a natural equivalence relation) of holomorphic maps, with connected fibers, of $X$ onto smooth curves of a fixed genus $>1$ is a topological invariant of $X$. In fact it depends only on the fundamental group of $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1992-04-01T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higgs line bundles",
      "kähler manifolds",
      "green-lazarsfeld sets",
      "holomorphic maps",
      "fundamental group"
    ],
    "tags": [
      "journal article",
      "expository article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Bull. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1992math......4225A"
    }
  }
}