{
  "id": "1703.07516",
  "version": "v1",
  "published": "2017-03-22T04:35:35.000Z",
  "updated": "2017-03-22T04:35:35.000Z",
  "title": "Irreducibility of the Hilbert scheme of smooth curves in $\\Bbb P^4$ of degree $g+2$ and genus $g$",
  "authors": [
    "Changho Keem",
    "Yun-Hwan Kim"
  ],
  "comment": "Any critical comments are welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "We denote by $\\mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree $d$ and genus $g$ in $\\PP^r$. In this note, we show that any non-empty $\\mathcal{H}_{g+2,g,4}$ is irreducible without any restriction on the genus $g$. Our result augments the irreducibility result obtained earlier by Hristo Iliev(2006), in which several low genus $g\\le 10$ cases have been left untreated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-22T04:35:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14C05"
    ],
    "keywords": [
      "smooth curves",
      "hilbert scheme",
      "general point corresponds",
      "low genus",
      "non-degenerate curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}