{
  "id": "1406.5788",
  "version": "v2",
  "published": "2014-06-23T01:27:14.000Z",
  "updated": "2014-11-28T05:10:33.000Z",
  "title": "Local Fourier transform and blowing up",
  "authors": [
    "Kazuki Hiroe"
  ],
  "comment": "25 pages. Some typos and mathematical errors are corrected. A new section for the Stokes structures is add",
  "categories": [
    "math.CA",
    "math.AG"
  ],
  "abstract": "We consider a resolution of ramified irregular singularities of meromorphic connections on a formal disk via local Fourier transforms. A necessary and sufficient condition for an irreducible connection to have a resolution of the ramified singularity is determined as an analogy of the blowing up of plane curve singularities. We also relate the irregularity of Komatsu and Malgrange of connections to the intersection numbers and the Milnor numbers of plane curve germs. Finally, we shall define an analogue of Puiseux characteristics for connections and find an invariant of the family of connections with the fixed Puiseux characteristic by means of the structure of iterated torus knots of the plane curve germs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-23T01:27:14.000Z",
      "abstract": "We consider a resolution of ramified irregular singularities of meromorphic connections on a formal disk via local Fourier transforms. A necessary and sufficient condition for an irreducible connection to have a resolution of the ramified singularity is determined as an analogy of the blowing up of plane curve singularities. We also relate the irregularity of Komatsu and Malgrange of connections to the intersection numbers and the Milnor numbers of plane curve germs.",
      "comment": "15 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-28T05:10:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local fourier transform",
      "singularity",
      "plane curve singularities",
      "plane curve germs",
      "meromorphic connections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.5788H"
    }
  }
}