The weak Markus--Yamabe conjecture fails in dimension 14
Algebraic Geometry
2026-08-05 v1 Dynamical Systems
Abstract
We show that the weak Markus--Yamabe conjecture fails in every dimension . We first prove a chain realization theorem: every polynomial Keller map of with component degrees yields an explicit polynomial vector field on , with , whose Jacobian matrix has spectrum at every point and whose singularities are in bijection with any prescribed fiber of . Applied to the recent counterexample to the Jacobian conjecture, this gives a Hurwitz vector field of degree seven on with three rational singularities. A rank-reduced dehomogenization of the associated cubic stabilization gives, independently, a Hurwitz field of degree three on . The dimensions remain open.
Keywords
Cite
@article{arxiv.2608.05392,
title = {The weak Markus--Yamabe conjecture fails in dimension 14},
author = {Álvaro Castañeda and Gerardo Honorato and Francisco Valenzuela-Henríquez},
journal= {arXiv preprint arXiv:2608.05392},
year = {2026}
}