{
  "id": "2102.01056",
  "version": "v1",
  "published": "2021-02-01T18:46:39.000Z",
  "updated": "2021-02-01T18:46:39.000Z",
  "title": "Wall-crossing for zero-dimensional sheaves and Hilbert schemes of points on Calabi--Yau 4-folds",
  "authors": [
    "Arkadij Bojko"
  ],
  "categories": [
    "math.AG",
    "math.KT",
    "math.RT"
  ],
  "abstract": "We define a vertex algebra on the moduli stack of the auxiliary abelian category of pairs to give a precise formulation of the wall-crossing conjecture for Calabi--Yau 4-folds proposed by Gross--Joyce--Tanaka arXiv:2005.05637. Assuming that it holds, we prove the conjecture of Cao--Kool arXiv:1712.07347 for 0-dimensional DT4 invariants on projective Calabi--Yau 4-folds. We also give formulae for generating series of topological virtual fundamental classes of Hilbert schemes of points and 0-dimensional sheaves. Using these, we prove a version of Nekrasov's conjecture arXiv:1712.08128 for compacts and its generalization to K-theory classes of higher rank. We compute higher rank Segre series. After defining the correct generalization of virtual Verlinde series for 4-folds, we obtain a very simple Segre--Verlinde correspondence. Finally, we relate universal series of general invariants for elliptic surfaces and elliptic curves to those on CY 4-folds via a universal transformation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-01T18:46:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert schemes",
      "zero-dimensional sheaves",
      "calabi-yau",
      "higher rank segre series",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}