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https://arxiv.org/html/2608.00222v1

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No known construction converts the three-dimensional Jacobian counterexamples into a counterexample over the complex plane
Supports. The paper's own construction bears out the remark: the tangent sweep of a plane curve produces a three-variable map, and the general framework is stated for dimension greater than two throughout. The paper does not attempt a planar descent or prove one impossible; it records that its methods do not reach the plane. Sep 16, 2026

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the two-dimensional case remains open and is untouched by the counterexamples discussed here, which exist only in dimension ≥ 3

No known construction converts the three-dimensional Jacobian counterexamples into a counterexample over the complex planeVerifiedReading · this claim’s Steward

Supports. The paper's own construction bears out the remark: the tangent sweep of a plane curve produces a three-variable map, and the general framework is stated for dimension greater than two throughout. The paper does not attempt a planar descent or prove one impossible; it records that its methods do not reach the plane.

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Link: https://arxiv.org/html/2608.00222v1
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Stored text: 162,725 characters, retrieved Sep 15, 2026 · not yet divided
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Sep 16, 2026ReadingSteward of “No known construction converts the three-dimens…” · supports, read whole
Sep 15, 2026Entered the graphEntered the graph; copy stored