{
  "annotation_id": "412cfce9-d98c-454c-9328-8961990497f6",
  "date_created": "2026-03-02T18:02:50.878000Z",
  "date_modified": "2026-03-02T18:02:50.878000Z",
  "file_hash": "f4a9aff2b55084f922e6f0624ee25dc2d38c061ff47fe9f47ce237b9cdf0a495",
  "private": false,
  "record": {
    "abstract": "We study the geometrical meaning of the Faa\u0027 di Bruno polynomials in the\ncontext of KP theory. They provide a basis in a subspace W of the universal\nGrassmannian associated to the KP hierarchy. When W comes from geometrical data\nvia the Krichever map, the Faa\u0027 di Bruno recursion relation turns out to be the\ncocycle condition for (the Welters hypercohomology group describing) the\ndeformations of the dynamical line bundle on the spectral curve together with\nthe meromorphic sections which give rise to the Krichever map. Starting from\nthis, one sees that the whole KP hierarchy has a similar cohomological meaning.",
    "arxiv_id": "solv-int/9704010",
    "authors": [
      "Gregorio Falqui",
      "Cesare Reina",
      "Alessandro Zampa"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "Krichever Maps, Faa\u0027 di Bruno Polynomials, and Cohomology in KP Theory",
    "url": "https://arxiv.org/abs/solv-int/9704010"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a6b212b6-944e-42e7-a6eb-93ec0deca2d1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}