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July 26, 2026Open Access

The Alpöge counterexample to the Jacobian Conjecture: affine chart certificates and bounded rigidity computations

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Authors

ARAdrian Rodriguez Rodriguez

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Overview

Counterexample to the Jacobian Conjecture shows unique structures in affine charts, indicating bounded rigidity implications.

Key Points

  • This study investigates the counterexample to the Jacobian Conjecture in dimension 3, focusing on affine chart descriptions and bounded rigidity.
  • Utilized explicit affine resultant-subresultant certificates for cubic equations.
  • Conducted bounded rigidity computations within parametrized families and verified ideal inclusions with Gröbner bases.
  • Presented a graded analysis of viable kernels and explored the empty candidate cone-degree sectors.
  • Identified non-properness in the affine chart due to conditions defined by parameter L.
  • Proved that kernels for specific degrees are empty, suggesting unique behaviors in the counterexample.
  • Challenged existing theories by questioning the generic degree of non-invertible Keller maps.

Cite This Study

Adrian Rodriguez Rodriguez (2026) studied this question.

synapsesocial.com/papers/6a65a36cd3aea3239cd7693fhttps://doi.org/10.5281/zenodo.21517226
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