{
  "id": "2102.11170",
  "version": "v1",
  "published": "2021-02-22T16:48:50.000Z",
  "updated": "2021-02-22T16:48:50.000Z",
  "title": "Stability of the tangent bundle through conifold transitions",
  "authors": [
    "Tristan C. Collins",
    "Sebastien Picard",
    "Shing-Tung Yau"
  ],
  "comment": "80 pages, 1 appendix",
  "categories": [
    "math.DG",
    "hep-th",
    "math.AG"
  ],
  "abstract": "Let $X$ be a compact, K\\\"ahler, Calabi-Yau threefold and suppose $X\\mapsto \\underline{X}\\leadsto X_t$ , for $t\\in \\Delta$, is a conifold transition obtained by contracting finitely many disjoint $(-1,-1)$ curves in $X$ and then smoothing the resulting ordinary double point singularities. We show that, for $|t|\\ll 1$ sufficiently small, the tangent bundle $T^{1,0}X_{t}$ admits a Hermitian-Yang-Mills metric $H_t$ with respect to the conformally balanced metrics constructed by Fu-Li-Yau. Furthermore, we describe the behavior of $H_t$ near the vanishing cycles of $X_t$ as $t\\rightarrow 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-22T16:48:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tangent bundle",
      "conifold transition",
      "resulting ordinary double point singularities",
      "calabi-yau threefold",
      "hermitian-yang-mills metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 80,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}