trailNon-invertible constant-Jacobian polynomial self-maps of ℂ³ exist in every geometric degree at least three
Gallagher's explicit degree family· for
Alpöge's map (a,b,c) on ℂ³ has constant Jacobian determinant −2 yet is generically three-to-one
bedrock · fact
Gallagher's July 2026 construction yields a generically d-to-one Keller map of C³ for every integer d at least three
atomic
The geometric tangent-sweep route· for
In the 2026 Jacobian-counterexample construction, the complement of the ramification divisor and hyperplane preimage in P¹×P² is isomorphic to affine three-space.
atomic
Gao's tangent-sweep construction produces constant-Jacobian counterexamples of arbitrarily large geometric degree in every dimension greater than two
atomic
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Non-invertible constant-Jacobian polynomial self-maps of ℂ³ exist in every geometric degree at least three
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