{
  "id": "2404.08840",
  "version": "v1",
  "published": "2024-04-12T23:01:00.000Z",
  "updated": "2024-04-12T23:01:00.000Z",
  "title": "On Nash resolution of (singular) Lie algebroids",
  "authors": [
    "Ruben Louis"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "Any Lie algebroid $A$ admits a Nash-type blow-up $\\mathrm{Nash}(A)$ that sits in a nice short exact sequence of Lie algebroids $0\\rightarrow K\\rightarrow \\mathrm{Nash}(A)\\rightarrow \\mathcal{D}\\rightarrow 0$ with $K$ a Lie algebra bundle and $\\mathcal{D}$ a Lie algebroid whose anchor map is injective on an open dense subset. The base variety is a blowup determined by the singular foliation of $A$. We provide concrete examples. Moreover, we extend the construction following Mohsen's to singular subalgebroids in the sense of Androulidakis-Zambon.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-12T23:01:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D17",
      "32S45"
    ],
    "keywords": [
      "lie algebroid",
      "nash resolution",
      "nice short exact sequence",
      "lie algebra bundle",
      "open dense subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}