{
  "annotation_id": "90ac194f-b68a-4f6f-aa1c-8e56c4b8da90",
  "date_created": "2026-03-02T18:02:51.150000Z",
  "date_modified": "2026-03-02T18:02:51.150000Z",
  "file_hash": "2eae1fe7940524b18377c132914b60cd28efc687c590b0de11586e863dfb0b6d",
  "private": false,
  "record": {
    "abstract": "The asymptotic lattices and their transformations are studied within the line\ngeometry approach. It is shown that the discrete asymptotic nets are\nrepresented by isotropic congruences in the Plucker quadric. On the basis of\nthe Lelieuvre-type representation of asymptotic lattices and of the discrete\nanalog of the Moutard transformation, it is constructed the discrete analog of\nthe W-congruences, which provide the Darboux-Backlund type transformation of\nasymptotic lattices.The permutability theorems for the discrete Moutard\ntransformation and for the corresponding transformation of asymptotic lattices\nare established as well. Moreover, it is proven that the discrete W-congruences\nare represented by quadrilateral lattices in the quadric of Plucker. These\nresults generalize to a discrete level the classical line-geometric approach to\nasymptotic nets and W-congruences, and incorporate the theory of asymptotic\nlattices into more general theory of quadrilateral lattices and their\nreductions.",
    "arxiv_id": "solv-int/9909015",
    "authors": [
      "Adam Doliwa"
    ],
    "categories": [
      "solv-int",
      "math.DG",
      "nlin.SI"
    ],
    "doi": "10.1016/S0393-0440(00)00070-X",
    "journal_ref": "J. Geom. Phys. 39 (2001) 9-29",
    "title": "Discrete asymptotic nets and W-congruences in Plucker line geometry",
    "url": "https://arxiv.org/abs/solv-int/9909015"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9a88bccd-be65-49d9-9c3e-0bf613aae20f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}