{
  "schema_version": 1,
  "problem_number": "AIM-SEVERAL_COMPLEX_VARIABLES-0028",
  "title": "Algebraic Zero Curves of Homogeneous Plurisubharmonic Polynomials",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "Let p be a nonzero homogeneous plurisubharmonic polynomial on C^2. Every irreducible affine algebraic curve avoiding the origin on which p vanishes is exactly a nonzero level of a homogeneous holomorphic polynomial of degree at most degree(p). No smoothness or rationality assumption is needed. The proof eliminates polar leading terms on the compact normalization, then uses complex dilations, polarization and binary-form irreducibility. If reducible curves are allowed, a degree-eight counterexample exists even without pluriharmonic terms.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.CV",
    "math.AG"
  ],
  "keywords": [
    "plurisubharmonic polynomials",
    "algebraic curves",
    "homogeneous polynomials",
    "Levi form",
    "normalization",
    "AIM-SEVERAL_COMPLEX_VARIABLES-0028"
  ],
  "manuscript_version_date": "2026-10-05",
  "publication_date": "2026-10-05",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-05",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-several_complex_variables-0028/",
  "pdf_url": "https://eulersolve.org/papers/aim-several_complex_variables-0028/paper.pdf?v=482eba592969",
  "doi": "10.5281/zenodo.23162700",
  "zenodo_record_url": "https://zenodo.org/records/23162700",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete all-degree irreducible-curve theorem and an explicit reducible counterexample for the zero-curve question of Stensones in the 2010 AIM workshop list, recorded as AIM-SEVERAL_COMPLEX_VARIABLES-0028. Both curve conventions are addressed. No claim is made about the adjacent Newton-diagram problem or nonalgebraic curves. The upstream quadratic case and elementary reducible obstruction are credited prior observations. The written general proof is distinct from the 39 exact regression checks. AI-assisted, self-audited and unrefereed; no independent review or proof-assistant formalization is claimed. Novelty and absolute priority remain undetermined after a bounded primary-source comparison.",
  "files": {
    "paper.pdf": {
      "sha256": "482eba59296933af01bc00819266b781bb2fd697e1250265427182a2f813a889"
    },
    "source.zip": {
      "sha256": "b321e395cb6f9bf69a1ef28fadbe5f9f6d03c1faf323be63b6fb53833edcb8eb"
    },
    "verification_report.md": {
      "sha256": "75b76b264f5745f7e40b997f500d77fd4c8223d54e827836b838e1489fe85bca"
    }
  },
  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}