{
  "id": "2404.15066",
  "version": "v1",
  "published": "2024-04-23T14:13:35.000Z",
  "updated": "2024-04-23T14:13:35.000Z",
  "title": "Maximal Brill-Noether loci via degenerations and double covers",
  "authors": [
    "Andrei Bud",
    "Richard Haburcak"
  ],
  "comment": "16 pages, comments welcome! MPIM-Bonn-2024",
  "categories": [
    "math.AG"
  ],
  "abstract": "Using limit linear series on chains of curves, we show that closures of certain Brill-Noether loci contain a product of pointed Brill-Noether loci of small codimension. As a result, we obtain new non-containments of Brill-Noether loci, in particular that dimensionally expected non-containments hold for expected maximal Brill-Noether loci. Using these degenerations, we also give a new proof that Brill-Noether loci with expected codimension $-\\rho\\leq \\lceil g/2 \\rceil$ have a component of the expected dimension. Additionally, we obtain new non-containments of Brill-Noether loci by considering the locus of the source curves of unramified double covers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-23T14:13:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H51",
      "14H10"
    ],
    "keywords": [
      "double covers",
      "degenerations",
      "limit linear series",
      "expected maximal brill-noether loci",
      "brill-noether loci contain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}