{
  "id": "2105.09340",
  "version": "v1",
  "published": "2021-05-19T18:02:52.000Z",
  "updated": "2021-05-19T18:02:52.000Z",
  "title": "Linear series on general curves with prescribed incidence conditions",
  "authors": [
    "Gavril Farkas",
    "Carl Lian"
  ],
  "comment": "14 pages, comments welcome",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "Using degeneration and Schubert calculus, we consider the problem of computing the number of linear series of given degree d and dimension r on a general curve of genus g satisfying prescribed incidence conditions at n points. We determine these numbers completely for linear series of arbitrary dimension when d is sufficiently large, and for all d when either r=1 or n=r+2. Our formulas generalize and give new proofs of recent results of Tevelev and of Cela-Pandharipande-Schmitt.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-19T18:02:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear series",
      "general curve",
      "schubert calculus",
      "arbitrary dimension",
      "satisfying prescribed incidence conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}