{
  "abstract": "We study algebraic relations among functions in star-invariant subspaces. Let $θ$ be an inner function and suppose that $f,g,h\\in K_θ^p$ satisfy $P(f,g,h)=0$, in which $P$ is a homogeneous polynomial and the associated projective plane curve is smooth. Then $\\dim\\operatorname{span}\\{f,g,h\\}\\leq1$ if either $\\operatorname{deg} P\\geq 4$ and the boundary spectrum of $θ$ has logarithmic capacity zero, or $\\operatorname{deg} P = 3$ and the boundary spectrum contains at most one point. This settles new cases of a problem of Dyakonov, subsumes the previously known results, and recovers the classical fact that polynomial parametrizations of a smooth projective plane curve of degree at least three are projectively constant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17180",
  "author_total": 1,
  "authors": [
    {
      "name": "Stephan Ramon Garcia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53ag08r677qd0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17180",
  "fulltext_url": null,
  "id": "53ag08r677qd0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17180",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7221827610",
  "pdf_url": "https://arxiv.org/pdf/2610.17180",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53ag08r677qd0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17180",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17180"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Fermat's Last Theorem in star-invariant subspaces II: small boundary spectrum, projective plane curves, and the cubic Fermat equation",
  "title_text": "Fermat's Last Theorem in star-invariant subspaces II: small boundary spectrum, projective plane curves, and the cubic Fermat equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/53ag08r677qd0",
  "venue": "arXiv",
  "versions": []
}