{
  "id": "2212.05859",
  "version": "v1",
  "published": "2022-12-12T12:50:55.000Z",
  "updated": "2022-12-12T12:50:55.000Z",
  "title": "On Rigid Manifolds of Kodaira Dimension 1",
  "authors": [
    "Ingrid Bauer",
    "Christian Gleissner",
    "Julia Kotonski"
  ],
  "comment": "24 pages, 1 figure, code on personal webpage",
  "categories": [
    "math.AG"
  ],
  "abstract": "We discuss rigid compact complex manifolds of Kodaira dimension 1, arising as product-quotient varieties. First, we show that there is no free rigid action on the product of $(n-1)$ elliptic curves and a curve of genus at least two. Then, we describe the occurring groups, study the quotients and prove that there is always a suitable resolution of singularities preserving rigidity. Finally, we give a complete classification of the cases arising for minimal group orders.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-12T12:50:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32G05",
      "14L30",
      "14J10",
      "14J40",
      "14M25",
      "14B05"
    ],
    "keywords": [
      "kodaira dimension",
      "rigid manifolds",
      "rigid compact complex manifolds",
      "free rigid action",
      "minimal group orders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}