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TopicsAlpöge's ℂ³ map Algebraic geometry Jacobian conjecture

The Alpöge–Fable polynomial map F:ℂ³→ℂ³ has constant Jacobian determinant −2 yet sends three distinct points to a common image.

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An Independent Lean 4 Verification of the Alpöge–Fable Counterexample Untraced · nothing upstream recorded

The claim, due to Alpöge and Fable: det Jac F ≡ −2 identically, and F(0, 0, −1/4) = F(1, −3/2, 13/2) = F(−1, 3/2, 13/2) = (−1/4, 0, 0).

An Independent Lean 4 Verification of the Alpöge–Fable Counterexampleextraction 0.90

§1, defining the polynomial map F=(P,Q,R):ℂ³→ℂ³ presented as a counterexample

The claim, due to Alpöge and Fable: det Jac F ≡ −2 identically, and F(0, 0, −1/4) = F(1, −3/2, 13/2) = F(−1, 3/2, 13/2) = (−1/4, 0, 0).

An Independent Lean 4 Verification of the Alpöge–Fable Counterexampleextraction 0.90

§1, defining the polynomial map F = (P, Q, R) : ℂ³ → ℂ³ and asserting it is a Jacobian Conjecture counterexample.

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Created by extractor · Sep 16, 2026. Every judgment on this page is accompanied by a reasoning trace.