{
  "id": "2201.03833",
  "version": "v3",
  "published": "2022-01-11T08:31:17.000Z",
  "updated": "2022-10-13T07:02:02.000Z",
  "title": "Universality of Descendent Integrals over Moduli Spaces of Stable Sheaves on $K3$ Surfaces",
  "authors": [
    "Georg Oberdieck"
  ],
  "journal": "SIGMA 18 (2022), 076, 15 pages",
  "doi": "10.3842/SIGMA.2022.076",
  "categories": [
    "math.AG"
  ],
  "abstract": "We interprete results of Markman on monodromy operators as a universality statement for descendent integrals over moduli spaces of stable sheaves on $K3$ surfaces. This yields effective methods to reduce these descendent integrals to integrals over the punctual Hilbert scheme of the $K3$ surface. As an application we establish the higher rank Segre-Verlinde correspondence for $K3$ surfaces as conjectured by G\\\"ottsche and Kool.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-10-13T07:02:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "descendent integrals",
      "moduli spaces",
      "stable sheaves",
      "higher rank segre-verlinde correspondence",
      "punctual hilbert scheme"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}