{
  "id": "2501.07675",
  "version": "v1",
  "published": "2025-01-13T20:19:29.000Z",
  "updated": "2025-01-13T20:19:29.000Z",
  "title": "On the stability of holomorphic families of endomorphisms of ${\\mathbb P}^k$",
  "authors": [
    "François Berteloot",
    "Xavier Buff"
  ],
  "comment": "7 pages",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "In the context of holomorphic families of ${\\mathbb P}^k$ endomorphisms, we show that various notions of stability are equivalent. This allows us to both extend and simplify the architecture of the proof of certain results of [BBD]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-13T20:19:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32H50",
      "32U40",
      "37F45"
    ],
    "keywords": [
      "holomorphic families",
      "endomorphisms",
      "equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}