{
  "id": "math/0403409",
  "version": "v1",
  "published": "2004-03-24T10:52:19.000Z",
  "updated": "2004-03-24T10:52:19.000Z",
  "title": "Geometric interplay between function subspaces and their rings of differential operators",
  "authors": [
    "Rikard Bögvad",
    "Rolf Källström"
  ],
  "comment": "36 pages, LaTeX",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "We study, in the setting of algebraic varieties, finite-dimensional spaces of functions V that are invariant under a ring D^V of differential operators, and give conditions under which D^V acts irreducibly. We show how this problem, originally formulated in physics (Kamran-Milson-Olver), is related to the study of principal parts bundles and Weierstrass points (Laksov-Thorup), including a detailed study of Taylor expansions. Under some conditions it is possible to obtain V and D^V as global sections of a line bundle and its ring of differential operators. We show that several of the published examples of D^V are of this type, and that there are many more -- in particular arising from toric varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-03-24T10:52:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "differential operators",
      "geometric interplay",
      "function subspaces",
      "principal parts bundles",
      "line bundle"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3409B"
    }
  }
}