{
  "id": "1404.4291",
  "version": "v2",
  "published": "2014-04-16T15:51:33.000Z",
  "updated": "2014-05-30T16:18:48.000Z",
  "title": "(0,2)-Deformations and the $G$-Hilbert Scheme",
  "authors": [
    "Benjamin Gaines"
  ],
  "comment": "20 pages, 7 figures",
  "categories": [
    "math.AG",
    "hep-th"
  ],
  "abstract": "We study first order deformations of the tangent sheaf of resolutions of Calabi-Yau threefolds that are of the form $\\mathbb{C}^3/Z_r$, focusing on the cases where the orbifold has an isolated singularity. We prove a lower bound on the number of deformations for any crepant resolution of this orbifold. We show that this lower bound is achieved when the resolution used is the G-Hilbert scheme, and note that this lower bound can be found using methods from string theory. These methods lead us to a new way to construct the G-Hilbert scheme using the singlet count.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-30T16:18:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bound",
      "study first order deformations",
      "g-hilbert scheme",
      "tangent sheaf",
      "singlet count"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1293930,
      "adsabs": "2014arXiv1404.4291G"
    }
  }
}