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Equivalence of the Four-Variable Hessian and Planar Jacobian Conjectures

A mix of human-written and AI-generated textHuman understanding: some partsmath.AG — Algebraic Geometrymath.AC — Commutative Algebra

Contributed by Qiyue Tang ↗

Version 1 / Nov 06, 2026 / CC BY 4.0

Abstract

We prove that the four-variable Hessian conjecture and the planar Jacobian conjecture are equivalent over the complex numbers.

Provenance statement

GPT-6-Pro was used to investigate the four-variable Hessian conjecture in three research runs of 7, 8, and 9 hours, totaling 24 hours of elapsed research time. In the third run, the author prompted GPT-6-Pro to examine the implications between the four-variable Hessian conjecture and the planar Jacobian conjecture. That investigation produced the equivalence proved in this paper. Codex was used to review the proofs and revise the exposition. A Rethlas-OSV review is planned, and its outcome will be reported once available.

References

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Version history

  1. v1 · 31 pagesSubmitted by Qiyue TangInitial depositCurrentNov 06, 2026