{
  "annotation_id": "76224e4b-1980-43de-8b5c-b3a369e948af",
  "date_created": "2026-03-02T18:01:28.070000Z",
  "date_modified": "2026-03-02T18:01:28.070000Z",
  "file_hash": "a2d7f75a1fc595c8d46107432fc1e625cc2d25622e7af1623f0c4e449c5d51c0",
  "private": false,
  "record": {
    "abstract": "The Poincare duality of classical cohomology and the extension of this\nduality to quantum cohomology endows these rings with the structure of a\nFrobenius algebra. Any such algebra possesses a canonical ``characteristic\nelement;\u0027\u0027 in the classical case this is the Euler class, and in the quantum\ncase this is a deformation of the classical Euler class which we call the\n``quantum Euler class.\u0027\u0027 We prove that the characteristic element of a\nFrobenius algebra A is a unit if and only if A is semisimple, and then apply\nthis result to the cases of the quantum cohomology of the finite complex\nGrassmannians, and to the quantum cohomology of hypersurfaces. In addition we\nshow that, in the case of the Grassmannians, the [quantum] Euler class equals,\nas [quantum] cohomology element and up to sign, the determinant of the Hessian\nof the [quantum] Landau-Ginzbug potential.",
    "arxiv_id": "q-alg/9712025",
    "authors": [
      "Lowell Abrams"
    ],
    "categories": [
      "q-alg",
      "alg-geom",
      "math.AG",
      "math.AT",
      "math.QA"
    ],
    "title": "The quantum Euler class and the quantum cohomology of the Grassmannians",
    "url": "https://arxiv.org/abs/q-alg/9712025"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "eb50a09e-da94-458f-96c7-22429e3b5452",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}