[
  {
    "id": "ARR-2026-4FYHCBAQ0T8FHRBT-v1",
    "type": "article",
    "title": "Prescribed Tjurina Algebras and Complete Spectra in Osculating-Absorbing Gauss Fibres",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          8,
          25
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-4FYHCBAQ0T8FHRBT",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-4FYHCBAQ0T8FHRBT/versions/v1/",
    "note": "Research preprint; ARR-2026-4FYHCBAQ0T8FHRBT v1. Not peer reviewed by AIRR.",
    "abstract": "Given d >= 1, 1 <= s <= m, N = binom(d+m,d), and any N isolated complex hypersurface germs g_i of order at least s+1, we construct, for every D >= 1 + sum_i(tau(g_i)+2), a smooth integral degree-D hypersurface with a tangent hyperplane whose reduced Gauss fibre has exactly N points, is point-span order-s osculating-absorbing, and has the prescribed completed Tjurina algebras. The fibre length is sum_i tau(g_i), and the dual multiplicity is sum_i mu(g_i). For surfaces, the classical complete Tjurina spectrum of ordinary plane multiple points yields every integer fibre length between binom(m+2,2) floor((3s^2+4s-3)/4) and binom(m+2,2)s^2 at fixed dual multiplicity. We also give a direct strong-Lefschetz proof that x^(s+1)+y^(s+1)+z^(s+1)+(x+y+z)^(s+2) attains Wahl's classical three-variable value s(s+2)(2s-1)/3, producing sharp absorbed threefold fibres. All claims are over C; degree bounds are sufficient, not asserted minimal, and no exhaustive priority or human peer-review claim is made."
  }
]