{
  "id": "2411.12546",
  "version": "v1",
  "published": "2024-11-19T14:55:45.000Z",
  "updated": "2024-11-19T14:55:45.000Z",
  "title": "On Hilbert scheme of complete intersection on the biprojective",
  "authors": [
    "Aislan Leal Fontes",
    "Maxwell Paixão"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "The goal of this paper is to construct the Hilbert scheme of complete intersections in the biprojective space $X=\\mathbb{P}^m\\times\\mathbb{P}^n$ and for this, we define a partial order on the bidegrees of the bihomogeneous forms. As a consequence of this construction, we computer explicitly the Hilbert scheme for curves of genus 7 and 8 listed in \\cite{MUK95} and \\cite{MUKIDE03} that are complete intersections. Finally, we construct the coarse moduli space of complete intersections in $\\mathbb{P}^1\\times\\mathbb{P}^1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-19T14:55:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D22",
      "14H10",
      "14C05",
      "14D20"
    ],
    "keywords": [
      "complete intersection",
      "hilbert scheme",
      "coarse moduli space",
      "partial order",
      "biprojective space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}