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arXiv · 2606.22041

An organizing principle in the study of the Jacobian Conjecture

Frederico Xavier
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Abstract

Let $\Omega$ be an irreducible component of the locus of polynomial maps $ F:\mathbb C^n \to \mathbb C^n$ satisfying $\text{\rm deg} F\leq k$ and $\text{det}DF=1$. It is shown that either $\Omega \subset \text{\rm Aut} (\mathbb C^n)$, as claimed by the Jacobian Conjecture, or the {\em general} $F\in \Omega$ is not an automorphism.

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Frederico Xavier. 2026-06-20. An organizing principle in the study of the Jacobian Conjecture. https://arxiv.org/abs/2606.22041

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