{
  "id": "2208.14351",
  "version": "v1",
  "published": "2022-08-30T15:55:23.000Z",
  "updated": "2022-08-30T15:55:23.000Z",
  "title": "Perverse sheaves on symmetric products of the plane",
  "authors": [
    "Tom Braden",
    "Carl Mautner"
  ],
  "comment": "45 pages",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "For any field $k$, we give an algebraic description of the category $\\mathrm{Perv}_\\mathscr{S}(S^n (\\mathbb{C}^2),k)$ of perverse sheaves on the $n$-fold symmetric product of the plane $S^n(\\mathbb{C}^2)$ constructible with respect to its natural stratification and with coefficients in $k$. As part of our description we obtain an analogue of modular Springer theory for the Hilbert scheme $\\mathrm{Hilb}^n(\\mathbb{C}^2)$ of $n$ points in the plane with its Hilbert-Chow morphism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-30T15:55:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perverse sheaves",
      "modular springer theory",
      "fold symmetric product",
      "natural stratification",
      "hilbert-chow morphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}