{
  "id": "1005.2053",
  "version": "v3",
  "published": "2010-05-12T11:26:06.000Z",
  "updated": "2013-06-19T14:28:37.000Z",
  "title": "Birkhoff strata of Sato Grassmannian and algebraic curves",
  "authors": [
    "B. G. Konopelchenko",
    "G. Ortenzi"
  ],
  "comment": "31 pages, no figures, version accepted in Journal of Nonlinear Mathematical Physics. The sections on the integrable systems present in previous versions has been published separately",
  "categories": [
    "math-ph",
    "math.AG",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "Algebraic and geometric structures associated with Birkhoff strata of Sato Grassmannian are analyzed. It is shown that each Birkhoff stratum $\\Sigma_S$ contains a subset $W_{\\hat{S}}$ of points for which each fiber of the corresponding tautological subbundle $TB_{W_S}$ is closed with respect to multiplication. Algebraically $TB_{W_S}$ is an infinite family of infinite-dimensional commutative associative algebras and geometrically it is an infinite tower of families of algebraic curves. For the big cell the subbundle $TB_{W_\\varnothing}$ represents the tower of families of normal rational (Veronese) curves of all degrees. For $W_1$ such tautological subbundle is the family of coordinate rings for elliptic curves. For higher strata, the subbundles $TB_{W_{1,2,\\dots,n}}$ represent families of plane $(n+1,n+2)$ curves (trigonal curves at $n=2$) and space curves of genus $n$. Two methods of regularization of singular curves contained in $TB_{W_{\\hat{S}}}$, namely, the standard blowing-up and transition to higher strata with the change of genus are discussed.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-06-19T14:28:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birkhoff stratum",
      "algebraic curves",
      "sato grassmannian",
      "higher strata",
      "tautological subbundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.2053K"
    }
  }
}