{
  "id": "1011.4205",
  "version": "v2",
  "published": "2010-11-18T14:54:11.000Z",
  "updated": "2011-02-03T16:05:04.000Z",
  "title": "Birkhoff strata of the Grassmannian Gr$\\mathrm{^{(2)}}$: Algebraic curves",
  "authors": [
    "B. G. Konopelchenko",
    "G. Ortenzi"
  ],
  "comment": "14 pages, no figures, improved some definitions, typos corrected",
  "categories": [
    "math-ph",
    "math.AG",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "Algebraic varieties and curves arising in Birkhoff strata of the Sato Grassmannian Gr${^{(2)}}$ are studied. It is shown that the big cell $\\Sigma_0$ contains the tower of families of the normal rational curves of all odd orders. Strata $\\Sigma_{2n}$, $n=1,2,3,...$ contain hyperelliptic curves of genus $n$ and their coordinate rings. Strata $\\Sigma_{2n+1}$, $n=0,1,2,3,...$ contain $(2m+1,2m+3)-$plane curves for $n=2m,2m-1$ $(m \\geq 2)$ and $(3,4)$ and $(3,5)$ curves in $\\Sigma_3$, $\\Sigma_5$ respectively. Curves in the strata $\\Sigma_{2n+1}$ have zero genus.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-02-03T16:05:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birkhoff strata",
      "algebraic curves",
      "contain hyperelliptic curves",
      "sato grassmannian gr",
      "normal rational curves"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s11232-011-0062-6",
      "journal": "Theoretical and Mathematical Physics",
      "year": 2011,
      "month": "Jun",
      "volume": 167,
      "number": 3,
      "pages": 785
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011TMP...167..785K"
    }
  }
}