{
  "id": "1806.02357",
  "version": "v1",
  "published": "2018-06-06T18:00:13.000Z",
  "updated": "2018-06-06T18:00:13.000Z",
  "title": "Complex hypersurfaces in a direct product of Riemann surfaces",
  "authors": [
    "Claudio Llosa Isenrich"
  ],
  "comment": "15 pages",
  "categories": [
    "math.GT",
    "math.AG",
    "math.GR"
  ],
  "abstract": "We study smooth complex hypersurfaces in a direct product of closed hyperbolic Riemann surfaces and give a classification in terms of their fundamental group. This answers a question of Delzant and Gromov on subvarieties of products of Riemann surfaces in the smooth codimension one case. We also answer Delzant and Gromov's question of which subgroups of a direct product of surface groups are K\\\"ahler for two classes: subdirect products of three surface groups; and subgroups arising as kernel of a homomorphism from the product of surface groups to $\\mathbb{Z}^3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-06T18:00:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32J27",
      "32Q15",
      "20F65",
      "20J05"
    ],
    "keywords": [
      "surface groups",
      "study smooth complex hypersurfaces",
      "closed hyperbolic riemann surfaces",
      "subdirect products",
      "fundamental group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}