{
  "id": "1811.01888",
  "version": "v1",
  "published": "2018-11-05T18:06:58.000Z",
  "updated": "2018-11-05T18:06:58.000Z",
  "title": "Narrow quantum D-modules and quantum Serre duality",
  "authors": [
    "Mark Shoemaker"
  ],
  "comment": "40 pages, comments welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "Given Y a non-compact manifold or orbifold, we define a natural subspace of the cohomology of Y called the narrow cohomology. We show that despite Y being non-compact, there is a well-defined and non-degenerate pairing on this subspace. The narrow cohomology proves useful for the study of genus zero Gromov-Witten theory. When Y is a smooth complex variety or Deligne-Mumford stack, one can define a quantum D-module on the narrow cohomology of Y. This yields a new formulation of quantum Serre duality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-05T18:06:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N35",
      "14E16",
      "53D45"
    ],
    "keywords": [
      "quantum serre duality",
      "narrow quantum d-modules",
      "narrow cohomology",
      "genus zero gromov-witten theory",
      "smooth complex variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}