{
  "id": "2209.05029",
  "version": "v1",
  "published": "2022-09-12T05:23:54.000Z",
  "updated": "2022-09-12T05:23:54.000Z",
  "title": "Horosymmetric limits of Kähler-Ricci flow on Fano $G$-manifolds",
  "authors": [
    "Gang Tian",
    "Xiaohua Zhu"
  ],
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "In this paper, we prove that on a Fano $\\mathbf G$-manifold $(M,J)$, the Gromov-Hausdorff limit of K\\\"ahler-Ricci flow with initial metric in $2\\pi c_1(M)$ must be a $\\mathbb Q$-Fano horosymmetric variety $M_\\infty$ which admits a singular K\\\"ahler-Ricci soliton. Moreover, we show that $M_\\infty$ is a limit of $\\mathbb C^*$-degeneration of $(M,J)$ induced by the soliton holomorphic vector field. A similar result can be also proved for K\\\"ahler-Ricci flows on any Fano horosymmetric manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-12T05:23:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "32Q20",
      "58D25",
      "14L10"
    ],
    "keywords": [
      "kähler-ricci flow",
      "horosymmetric limits",
      "soliton holomorphic vector field",
      "fano horosymmetric variety",
      "fano horosymmetric manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}