{
  "id": "2005.13372",
  "version": "v1",
  "published": "2020-05-27T14:06:42.000Z",
  "updated": "2020-05-27T14:06:42.000Z",
  "title": "Galois subspaces for smooth projective curves",
  "authors": [
    "Robert Auffarth",
    "Sebastián Rahausen"
  ],
  "comment": "16 pages including appendix. Comments are welcome!",
  "categories": [
    "math.AG"
  ],
  "abstract": "Given an embedding of a smooth projective curve $X$ of genus $g\\geq1$ into $\\mathbb{P}^N$, we study the locus of linear subspaces of $\\mathbb{P}^N$ of codimension 2 such that projection from said subspace, composed with the embedding, gives a Galois morphism $X\\to\\mathbb{P}^1$. For genus $g\\geq2$ we prove that this locus is a smooth projective variety with components isomorphic to projective spaces. If $g=1$ and the embedding is given by a complete linear system, we prove that this locus is also a smooth projective variety whose positive-dimensional components are isomorphic to projective bundles over \\'etale quotients of the elliptic curve, and we describe these components explicitly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-27T14:06:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smooth projective curve",
      "galois subspaces",
      "smooth projective variety",
      "complete linear system",
      "components isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}