{
  "id": "1704.06957",
  "version": "v1",
  "published": "2017-04-23T18:24:50.000Z",
  "updated": "2017-04-23T18:24:50.000Z",
  "title": "Entropy of an autoequivalence on Calabi-Yau manifolds",
  "authors": [
    "Yu-Wei Fan"
  ],
  "comment": "9 pages. Comments are welcome!",
  "categories": [
    "math.AG",
    "math.DS"
  ],
  "abstract": "We prove that the categorical entropy of the autoequivalence $T_{\\mathcal{O}}\\circ(-\\otimes\\mathcal{O}(-1))$ on a Calabi-Yau manifold is the unique positive real number $\\lambda$ satisfying $$ \\sum_{k\\geq 1}\\frac{\\chi(\\mathcal{O}(k))}{e^{k\\lambda}}=e^{(d-1)t}. $$ We then use this result to construct the first counterexamples of a conjecture on categorical entropy by Kikuta and Takahashi.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-23T18:24:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F05",
      "14J32",
      "18E30"
    ],
    "keywords": [
      "calabi-yau manifold",
      "autoequivalence",
      "categorical entropy",
      "unique positive real number",
      "first counterexamples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}