{
  "id": "1102.0700",
  "version": "v2",
  "published": "2011-02-03T15:19:50.000Z",
  "updated": "2011-05-31T16:23:21.000Z",
  "title": "Algebraic varieties in Birkhoff strata of the Grassmannian Gr$\\mathrm{^{(2)}}$: Harrison cohomology and integrable systems",
  "authors": [
    "B. G. Konopelchenko",
    "G. Ortenzi"
  ],
  "comment": "28 pages, no figures. Generally improved version, in particular the Discussion section. Added references. Corrected typos",
  "categories": [
    "math-ph",
    "math.AG",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "Local properties of families of algebraic subsets $W_g$ in Birkhoff strata $\\Sigma_{2g}$ of Gr$^{(2)}$ containing hyperelliptic curves of genus $g$ are studied. It is shown that the tangent spaces $T_g$ for $W_g$ are isomorphic to linear spaces of 2-coboundaries. Particular subsets in $W_g$ are described by the intergrable dispersionless coupled KdV systems of hydrodynamical type defining a special class of 2-cocycles and 2-coboundaries in $T_g$. It is demonstrated that the blows-ups of such 2-cocycles and 2-coboundaries and gradient catastrophes for associated integrable systems are interrelated.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-05-31T16:23:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birkhoff strata",
      "integrable systems",
      "grassmannian gr",
      "harrison cohomology",
      "algebraic varieties"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/44/46/465201",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2011,
      "month": "Nov",
      "volume": 44,
      "number": 46,
      "pages": 465201
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JPhA...44T5201K"
    }
  }
}