{
  "annotation_id": "d9ba1b6c-b462-4b94-9c56-46c7d35952f8",
  "date_created": "2026-03-02T18:02:50.900000Z",
  "date_modified": "2026-03-02T18:02:50.900000Z",
  "file_hash": "f90b5eebeff5965f5ae228437c2bae050177c458a9dd2ed21936214fc75b62b0",
  "private": false,
  "record": {
    "abstract": "We revisit the Hitchin integrable system whose phase space is the bundle\ncotangent to the moduli space $N$ of holomorphic $SL_2$-bundles over a smooth\ncomplex curve of genus two. $N$ may be identified with the 3-dimensional\nprojective space of theta functions of the second order, We prove that the\nHitchin system on $T^*N$ possesses a remarkable symmetry: it is invariant under\nthe interchange of positions and momenta. This property allows to complete the\nwork of van Geemen-Previato which, basing on the classical results on geometry\nof the Kummer quartic surfaces, specified the explicit form of the Hamiltonians\nof the Hitchin system. The resulting integrable system resembles the classic\nNeumann systems which are also self-dual. Its quantization produces a commuting\nfamily of differential operators of the second order acting on homogeneous\npolynomials in four complex variables. As recently shown by van Geemen-de Jong,\nthese operators realize the Knizhnik-Zamolodchikov-Bernard-Hitchin connection\nfor group SU(2) and genus 2 curves.",
    "arxiv_id": "solv-int/9710025",
    "authors": [
      "Krzysztof Gawedzki",
      "Pascal Tran-Ngoc-Bich"
    ],
    "categories": [
      "solv-int",
      "alg-geom",
      "hep-th",
      "math.AG",
      "nlin.SI"
    ],
    "doi": "10.1007/s002200050438",
    "title": "Self-duality of the SL_2 Hitchin integrable system at genus two",
    "url": "https://arxiv.org/abs/solv-int/9710025"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "506f0c91-979d-4004-8efa-6763868042bd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}