{
  "annotation_id": "dc1e68c2-2aa9-4f2b-9db4-6ced2b3fd38a",
  "date_created": "2026-02-17T05:53:26.430000Z",
  "date_modified": "2026-02-17T05:53:26.430000Z",
  "file_hash": "6f74fa927467f26867bb26075f495a8c2e945991ae61376eef215954b04ca204",
  "private": false,
  "record": {
    "abstract": "Complete hyperk\\\"ahler 4-manifolds of finite energy are grouped into ALE, ALF, ALG$^{(*)}$, ALH$^{(*)}$, each of these being further classified according to the Dynkin type of their noncompact end. A family of ALG-$D_4$ spaces are modeled by certain moduli spaces of strongly parabolic $\\mathrm{SL}(2,\\mathbb{C})$-Higgs bundles on the Riemann sphere with $n=4$ punctures. Meanwhile, a family of ALE-$D_4$ spaces are modeled by certain Nakajima quiver varieties known as $n=4$ hyperpolygon spaces. There is a map from hyperpolygon space to the moduli space of strong parabolic $\\mathrm{SL}(2,\\mathbb{C})$-Higgs bundles that is a diffeomorphism onto its open and dense image. We show that under a fine-tuned degenerate limit, the pullback of a family of ALG-$D_4$ metrics parameterized by $R$ converges pointwise to the ALE-$D_4$ metric as $R \\to 0$. While the connection to gravitational instantons occurs in the $n=4$ case, we prove our result for any finite $n$.",
    "arxiv_id": "2601.10656",
    "authors": [
      "Laura Fredrickson",
      "Arya Yae"
    ],
    "categories": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Hyperk\\\"ahler Degenerations from Parabolic $\\mathrm{SL}(2,\\mathbb{C})$-Higgs Bundles Moduli Spaces on the Punctured Sphere to Hyperpolygon Spaces",
    "url": "https://arxiv.org/abs/2601.10656",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a2141816-98b5-454f-9159-3be3068245b0",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}