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PreprintCC BY-NC-SA 4.0arXiv

Counterexamples to the Jacobian Conjecture from the viewpoint of lineability

  • L. Bernal-González
  • M. C. Calderón-Moreno
  • J. A. Prado-Bassas
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Abstract

Algebraic genericity in the family of polynomial counterexamples to the recently solved Jacobian Conjecture for N≥3 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.

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Cite

BibTeXRIS
BibTeX
@misc{bernalgonzalez2026counterexamples,
  title = {{Counterexamples to the Jacobian Conjecture from the viewpoint of lineability}},
  author = {L. Bernal-González and M. C. Calderón-Moreno and J. A. Prado-Bassas},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03572},
  eprint = {2611.03572},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03572},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Counterexamples to the Jacobian Conjecture from the viewpoint of lineability
AU  - L. Bernal-González
AU  - M. C. Calderón-Moreno
AU  - J. A. Prado-Bassas
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03572
UR  - https://arxiv.org/abs/2611.03572
AB  - Algebraic genericity in the family of polynomial counterexamples to the recently solved Jacobian Conjecture for N≥3 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.
ER  -