The two-variable Jacobian question

Statement

Every polynomial map F: ℂ² → ℂ² with constant nonzero Jacobian determinant has a polynomial inverse.

The source leaves this dimension open; the three-variable witness cannot be specialized to refute it.

Open

Complex dimension two.

Observed Oct 13, 2026

In this problem · publication v1

Different statement · related variant · Open

Relationship not independently reviewed. This concerns its use in this problem.

Introduction and analysis of the counterexample → · Original passage ↗
Recorded wording
Algebraic analysis of the three-variable counterexample, including its non-injectivity; the two-dimensional complex case remains open.
paraphrase · OpenMath supplies original paraphrases and links; no proof text is republished.

Shuhong Gao · Preprint · Publication date Jul 31, 2026

Public manuscript or exposition; publication does not imply independent OpenMath review.

Revision & attribution

Source revision: 2026-07-31. Observed Oct 13, 2026.

No AI contribution is asserted by this source record.

Source updated Jul 31, 2026.

Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.

Assessment history · 1

Assessments retained in these publication records. Earlier statement versions retain their own source histories.

Open

Complex dimension two.

Observed Oct 13, 2026 · Source passage →

Record details