trailEvery polynomial map of ℂ² with nonzero constant Jacobian determinant has a polynomial inverse
Every polynomial map of ℂⁿ with nonzero constant Jacobian determinant has a polynomial inverse
Planar partial results· for
The two-dimensional Jacobian conjecture holds for polynomial maps of degree at most 100
atomic
No known construction converts the three-dimensional Jacobian counterexamples into a counterexample over the complex plane
Every polynomial Keller map of the complex plane that is equivariant for a nontrivial multiplicative-group action is a polynomial automorphism
Vitushkin's construction method faces an obstruction in two dimensions that the three-dimensional polynomial counterexample circumvents
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A counterexample to the Jacobian conjecture in dimension n yields a counterexample in every dimension m ≥ n by adjoining identity coordinates
The two-dimensional Jacobian conjecture remains open
Collapse of the conjecture beyond the plane· against
The Jacobian conjecture is false in every dimension n ≥ 3
Alpöge's map (a,b,c) on ℂ³ has constant Jacobian determinant −2 yet is generically three-to-one
In the 2026 Jacobian-counterexample construction, the complement of the ramification divisor and hyperplane preimage in P¹×P² is isomorphic to affine three-space.
Gao's tangent-sweep construction produces constant-Jacobian counterexamples of arbitrarily large geometric degree in every dimension greater than two
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The separable Jacobian conjecture is false in dimension two in characteristic two.
Mondello's counterexample to the two-dimensional separable Jacobian conjecture in characteristic two is correct.
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Every polynomial map of ℂ² with nonzero constant Jacobian determinant has a polynomial inverse
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