{
  "id": "2010.01714",
  "version": "v1",
  "published": "2020-10-04T23:07:40.000Z",
  "updated": "2020-10-04T23:07:40.000Z",
  "title": "Arithmetic inflection formulae for linear series on hyperelliptic curves",
  "authors": [
    "Ethan Cotterill",
    "Ignacio Darago",
    "Changho Han"
  ],
  "comment": "22 pages, 4 figures",
  "categories": [
    "math.AG",
    "math.AT",
    "math.NT"
  ],
  "abstract": "Over the complex numbers, Pl\\\"ucker's formula computes the number of inflection points of a linear series of projective dimension $r$ and degree $d$ on a curve of genus $g$. Here we explore the geometric meaning of a natural analogue of Pl\\\"ucker's formula in $\\mathbb{A}^1$-homotopy theory for certain linear series on hyperelliptic curves defined over an arbitrary field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-04T23:07:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20",
      "14C35",
      "14N10",
      "14P25",
      "14Hxx",
      "11Gxx",
      "11Txx",
      "19E15"
    ],
    "keywords": [
      "linear series",
      "arithmetic inflection formulae",
      "hyperelliptic curves",
      "inflection points",
      "arbitrary field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}