trailEvery polynomial map of ℂⁿ with nonzero constant Jacobian determinant has a polynomial inverse
Alpöge's map (a,b,c) on ℂ³ has constant Jacobian determinant −2 yet is generically three-to-one
bedrock · fact
Every polynomial map of ℂ² with nonzero constant Jacobian determinant has a polynomial inverse
The two-dimensional Jacobian conjecture holds for polynomial maps of degree at most 100
The two-dimensional Jacobian conjecture is false in characteristic two.
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No known construction converts the three-dimensional Jacobian counterexamples into a two-dimensional counterexample
The Jacobian conjecture is false in every dimension n ≥ 3
atomic
claim · empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →claim page ↗︎
Every polynomial map of ℂⁿ with nonzero constant Jacobian determinant has a polynomial inverse
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