{
  "id": "1811.09741",
  "version": "v1",
  "published": "2018-11-24T01:49:36.000Z",
  "updated": "2018-11-24T01:49:36.000Z",
  "title": "Curves with prescribed symmetry and associated representations of mapping class groups",
  "authors": [
    "Marco Boggi",
    "Eduard Looijenga"
  ],
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "Let C be a complex smooth projective algebraic curve endowed with an action of a finite group G such that the quotient curve has genus at least 3. We prove that if the G-curve C is very general for these properties, then the natural map from the group algebra QG to the algebra of Q-endomorphisms of its Jacobian is an isomorphism. We use this to obtain (topological) properties regarding certain virtual linear representations of a mapping class group. For example, we show that the connected component of the Zariski closure of such a representation acts Q-irreducibly in a G-isogeny space of H^1(C; Q)and with image often a Q-almost simple group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-24T01:49:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H40",
      "14H37",
      "32G15"
    ],
    "keywords": [
      "mapping class group",
      "associated representations",
      "prescribed symmetry",
      "complex smooth projective algebraic curve",
      "virtual linear representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}