Randomized trial investigates the Jacobian Conjecture's counterexample in dimension 3, suggesting unique rigidity computations are crucial.
Key Points
This research aims to explore and analyze the counterexample to the Jacobian Conjecture presented by L. Alpöge, focusing on dimensionality and rigidity computations.
Analyzed cubic equations using affine resultant-subresultant certificates.
Conducted bounded rigidity computations with explicit parametrization and mutual ideal inclusion using Gröbner bases.
Organized viable kernels into an infinite tower based on graded analysis.
Identified the failure of the abscissa to separate fiber points at specific coordinates.
Confirmed that candidate cone-degree sectors for specified degrees (4, 5, 6) are empty in the graded range.
Motivated investigation into the nature of non-invertible z-linear Keller maps in relation to generic degree 3.
Cite This Study
Adrian Rodriguez Rodriguez (2026) studied this question.