{
  "id": "1912.13145",
  "version": "v1",
  "published": "2019-12-31T02:09:21.000Z",
  "updated": "2019-12-31T02:09:21.000Z",
  "title": "Collapsing of the line bundle mean curvature flow on Kähler surfaces",
  "authors": [
    "Ryosuke Takahashi"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study the line bundle mean curvature flow on K\\\"ahler surfaces under the hypercritical phase and a certain semipositivity condition. We naturally encounter such a condition when considering the blowup of K\\\"ahler surfaces. We show that the flow converges smoothly to a singular solution to the deformed Hermitian Yang-Mills equation away from a finite number of holomorphic curves of negative self-intersection on the surface.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-31T02:09:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C55",
      "53C44"
    ],
    "keywords": [
      "line bundle mean curvature flow",
      "kähler surfaces",
      "deformed hermitian yang-mills equation away"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}