Alpöge's counterexample to the JC, Economic Stabilization, and Zhao's Vanishing Conjecture
Michiel de Bondt
Source abstract
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.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.