{
  "id": "2006.09907",
  "version": "v1",
  "published": "2020-06-17T14:41:56.000Z",
  "updated": "2020-06-17T14:41:56.000Z",
  "title": "Extremal transitions via quantum Serre duality",
  "authors": [
    "Rongxiao Mi",
    "Mark Shoemaker"
  ],
  "comment": "53 pages, comments welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "Two varieties $Z$ and $\\widetilde Z$ are said to be related by extremal transition if there exists a degeneration from $Z$ to a singular variety $\\overline Z$ and a crepant resolution $\\widetilde Z \\to \\overline Z$. In this paper we compare the genus-zero Gromov--Witten theory of toric hypersurfaces related by extremal transitions arising from toric blow-up. We show that the quantum $D$-module of $\\widetilde Z$, after analytic continuation and restriction of a parameter, recovers the quantum $D$-module of $Z$. The proof provides a geometric explanation for both the analytic continuation and restriction parameter appearing in the theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-17T14:41:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N35",
      "14E16",
      "53D45"
    ],
    "keywords": [
      "quantum serre duality",
      "extremal transition",
      "analytic continuation",
      "genus-zero gromov-witten theory",
      "singular variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}