Counterexamples to the Jacobian Conjecture from the viewpoint of lineability

Algebraic genericity in the family of polynomial counterexamples to the recently solved Jacobian Conjecture for $N\ge3$ is investigated. The notion of affine-coneability is introduced and it is shown that this family is affine-coneable and 1-lineable, but not 2-lineable. Semigroupability is further studied with respect to coordinatewise multiplication and composition.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-02
DOI
https://doi.org/10.48550/arxiv.2611.03572
Primary Topic
Mathematical Dynamics and Fractals
Type
preprint
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preprint

Counterexamples to the Jacobian Conjecture from the viewpoint of lineability

L. Bernal-González, J. A. Prado-Bassas, M. C. Calderón-Moreno
arXiv (Cornell University)
Mathematical Dynamics and Fractals
preprint

Counterexamples to the Jacobian Conjecture from the viewpoint of lineability

L. Bernal-González, J. A. Prado-Bassas, M. C. Calderón-Moreno
preprint en

Abstract

Algebraic genericity in the family of polynomial counterexamples to the recently solved Jacobian Conjecture for $N\ge3$ is investigated. The notion of affine-coneability is introduced and it is shown that this family is affine-coneable and 1-lineable, but not 2-lineable. Semigroupability is further studied with respect to coordinatewise multiplication and composition.

arXiv (Cornell University)
Mathematical Dynamics and Fractals
DOIOpen Access PDFOpenAlex
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Counterexamples to the Jacobian Conjecture from the viewpoint of lineability — L. Bernal-González, J. A. Prado-Bassas, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS