{
  "annotation_id": "c04b5461-1a96-4269-817e-d4a9838f82e9",
  "date_created": "2026-02-17T05:53:04.785000Z",
  "date_modified": "2026-02-17T05:53:04.785000Z",
  "file_hash": "101fa5e8d260f6d885588fa8a06f998c1f177252e8d9f1fed833edb6ad2f8cf9",
  "private": false,
  "record": {
    "abstract": "We show a correspondence between the compact exceptional curves and divisors on $G-{\\rm Hilb}(\\mathbf{C}^3)$ and some non-trivial irreducible representations of $G \\subset GL(n,C)$ which are special (or essential). Moreover, we provide an explicit construction of the small resolution of $G-{\\rm Hilb}(\\mathbf{C}^3)$ and, using this resolution, we construct a correspondence between special and essential representations. These results are an extension of ``Special McKay correspondence\u0027\u0027 and ``Reid\u0027s recipe\u0027\u0027.",
    "arxiv_id": "2601.05634",
    "authors": [
      "Yukari Ito",
      "Kohei Sato",
      "Yusuke Sato"
    ],
    "categories": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Special vs Essential",
    "url": "https://arxiv.org/abs/2601.05634",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "588f4912-8ead-4cde-b163-7bc79a9fe0ee",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}