{
  "id": "2403.09934",
  "version": "v1",
  "published": "2024-03-15T00:23:56.000Z",
  "updated": "2024-03-15T00:23:56.000Z",
  "title": "Symmetric products of Galois-Maximal varieties",
  "authors": [
    "Javier Orts"
  ],
  "comment": "16 pages, 1 figure",
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "The main result of this paper is the proof that all the symmetric products of a finite Galois-Maximal space are Galois-Maximal spaces. This applies to the special case of real algebraic varieties, solving the problem first stated by Biswas and D'Mello in \\cite{biswas&d'mello:symmetric_products_M-curves} about symmetric products of Maximal curves. We also give characterisations of these spaces and state a new definition that generalises to a larger class of spaces. Then, we extend the characterisation in terms of the Borel cohomology given in \\cite{us} to the new family. Finally, we introduce the notion of cohomological stability and cohomological splitting, provide a systematic treatment and relate them with the properties of being a Maximal or Galois-Maximal space. These cohomological properties play an important role in the proof of our main theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-15T00:23:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F45",
      "14P25",
      "55N91"
    ],
    "keywords": [
      "symmetric products",
      "galois-maximal varieties",
      "finite galois-maximal space",
      "real algebraic varieties",
      "maximal curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}