{
  "id": "2402.01041",
  "version": "v2",
  "published": "2024-02-01T22:03:06.000Z",
  "updated": "2024-06-14T04:45:34.000Z",
  "title": "Unirationality of the universal moduli space of semistable bundles over smooth curves",
  "authors": [
    "Shubham Saha"
  ],
  "comment": "10 pages, comments welcome! (Remark 1 added in v2)",
  "categories": [
    "math.AG"
  ],
  "abstract": "We construct explicit dominant, rational morphisms from projective bundles over rational varieties to relevant moduli spaces, showing their unirationality. These constructions work for $U_{r,d,g}$; for all ranks, degrees and genus $2\\leq g \\leq 9$. Furthermore, the arguments presented also show that a similar conclusion can be made for $U_{r, \\mathcal{L}, g}$ for all $r,d$ and unirational $M_g$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-06-14T04:45:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "14H10"
    ],
    "keywords": [
      "universal moduli space",
      "smooth curves",
      "semistable bundles",
      "unirationality",
      "construct explicit dominant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}