{
  "id": "1907.03269",
  "version": "v1",
  "published": "2019-07-07T10:57:26.000Z",
  "updated": "2019-07-07T10:57:26.000Z",
  "title": "The homology of moduli stacks of complexes",
  "authors": [
    "Jacob Gross"
  ],
  "comment": "Comments welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "We compute the $E$-homology of the moduli stack $\\mathcal{M}$ of objects in the derived category of a smooth complex projective variety $X$, where $E$ is a complex-oriented homology theory with rational coefficient ring. For curves, surfaces, and some 3- and 4-folds we identify Joyce's vertex algebra construction on $E_\\ast(\\mathcal{M})$ with a generalised super-lattice vertex algebra associated to $K^0_{\\rm top}(X^{\\rm an}) \\oplus K^1_{\\rm top}(X^{\\rm an})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-07T10:57:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli stack",
      "identify joyces vertex algebra construction",
      "smooth complex projective variety",
      "generalised super-lattice vertex algebra",
      "rational coefficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}