Alpöge's counterexample to the JC, Economic Stabilization, and Zhao's Vanishing Conjecture

@misc{bondt2026alpöges,
  title = {{Alpöge's counterexample to the JC, Economic Stabilization, and Zhao's Vanishing Conjecture}},
  author = {Michiel de Bondt},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24889},
  eprint = {2610.24889},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24889},
}

TY  - UNPB
TI  - Alpöge's counterexample to the JC, Economic Stabilization, and Zhao's Vanishing Conjecture
AU  - Michiel de Bondt
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24889
UR  - https://arxiv.org/abs/2610.24889
AB  - In this paper, we apply stabilization techniques which are economic in the number of added dimensions to a slightly tweaked version of Alpöge's counterexample to JC(3) and JC(3,7). The first idea which lead to more economic stabilization is to bypass the degree 3 reduction of Bass, Connell and Wright in the construction of a counterexample to HJC(n). We construct counterexamples to HJC(15), VC(28), and HVC(30). On the other hand, we will perform degree 3 reduction after all to obtain counterexamples of low degree. We construct counterexamples to JC(12,3), HJC(18,3), VC(34,4), and HVC(36,4). As an encore, we construct a cubic-linear counterexample to the Jacobian Conjecture in dimension 90. All presented counterexamples to the Jacobian Conjecture (Vanishing Conjecture) are over the (Gaussian) integers.
ER  -