{
  "id": "2209.05906",
  "version": "v1",
  "published": "2022-09-13T11:41:27.000Z",
  "updated": "2022-09-13T11:41:27.000Z",
  "title": "Norm estimates for the $\\bar\\partial$-equation on a non-reduced space",
  "authors": [
    "Mats Andersson",
    "Richard Lärkäng"
  ],
  "comment": "28 pages",
  "categories": [
    "math.CV"
  ],
  "abstract": "We study norm-estimates for the $\\bar\\partial$-equation on non-reduced analytic spaces. Our main result is that on a non-reduced analytic space, which is Cohen-Macaulay and whose underlying reduced space is smooth, the $\\bar\\partial$-equation for $(0,1)$-forms can be solved with $L^p$-estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-13T11:41:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32A26",
      "32A27",
      "32B15",
      "32W05"
    ],
    "keywords": [
      "norm estimates",
      "non-reduced space",
      "non-reduced analytic space",
      "study norm-estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}